Question

a car covers 140 km distance with speed of 6 km/hr and the remaining distance with speed of 10km/hr. if it's reverses it's speed , it covers 8 km more in the same time. find the time taken by the car to cover 140 km and average speed of car.​

Answer 1

Answer :-

Average speed of car = 7.35 km/hr

Time taken by the car to cover 140 kilometres by average speed = 19. 04 hrs

GIVEN :-

• Car covers 140 km at speed of 6 km/hr

• It cover remaining distance at the speed of 10 km/hr

On reversing speed

• Car covers 140 kilometre at speed of 10 kilometre per hour .

• It covers remaining distance at speed of 6 kilometre per hour

• It also covers 8 km extra distance in the same time which it took to cover the distance before reversing speed .

• Time taken to cover both distances is same .

Solution :-

Let's assume that the total time taken by the car to cover these two distances is T hours , and remaining distance covered by car as x km .

So total distance covered 1st time is 140 + x km

Total distance covered 2nd time is 140 + x + 8 km

$\boxed{speed \: = \: \frac{distance}{time} }$

$\boxed{Time\: = \: \frac{ Distance}{Time} }$

Time taken to cover 1st distance .

Time taken to cover 140 km by 6 km/hr speed →

$Time \: = \: \frac{140}{6}$

Time = 23.34 hours .

Time taken to cover X kilometre by 10 km/hr speed

$Time \: = \: \frac{x}{10}$

Time = x/10 hours .......eq 1

Total time = 23.34 + X/10 hr.

Total time taken to cover 1st distance is 23.34 + X km/hr .

Time taken to cover second distance .

Time taken to cover 140 kilometre at the speed of 10 kilometre per hour .

$Time \: = \: \frac{140}{10}$

Time = 14 hours

Time taken to cover X kilometre at the speed of 6 kilometre per hour .

$Time \: = \: \frac{x}{6}$

Time = X/6 hours . .......eq 2

Time Taken to cover 8 kilometre at the speed of 60 km per hour .

$Time \: = \: \frac{8}{6}$

Time = 1.34 hours

Total time taken = 14 + 1.34 + X/6 hours

Total time taken to cover the second distance is 15.34 + X/6 hours

As it's given in the question that time taken for covering both distance is equivalent to each other .

→ Time taken to cover 1st distance = Time taken to cover 2nd distance.

→ 23 . 34 + X/10 = 15.34 + X/6

→ 23.34 - 15.34 = X/6 - X/10

→ 8 = (10x - 6x) / 60

→ 8 × 60 = 4x

→ 480/4 = x

→ X = 120 km

So the remaining distance given in the question is 120 kilometre.

Putting the value of x in equation 1

→ 120/ 10 = 12 hours

Total time taken to cover first distance = 23.34 + 12

→ Total time = 35 .34 hours ......eq 3rd

Putting the value of x in equation 2nd

→ 120/ 6 = 20 hours

Total time taken to cover second distance = 14 + 1.34 + 20

→ Total time = 35.34 hours ......eq 4th

So from equation third and fourth we conclude that time taken to cover both distances is equal to 35.34 hours

Total distance = 140 + 120 = 260 km

→ Average speed = Total distance/ total time taken

→ 260/ 35.34

→ Average speed = 7.35 km approx .

Now time taken to cover 140 kilometres at average speed →

→ 140/ 7.35 = 19 .04 hours .

Answer 2

________________________________

$\huge\tt{GIVEN:}$

• a car covers 140 km distance with speed of 6 km/hr
• and the remaining distance with speed of 10km/hr. if it's reverses it's speed
• it covers 8 km more in the same time.

________________________________

$\huge\tt{TO~FIND:}$

• the time taken by the car to cover 140 km
• average speed of car

________________________________

$\huge\tt{FORMULAS~USED:}$

• Speed = Distance/Time
• Time = Distance/Speed

________________________________

$\huge\tt{SOLUTION:}$

➡Let the total time taken by the car to cover the distance be P hours and the remaining distance by the car be x kms

Now,

➡Total distance covered in the first time would be (140 + x) km

➡And, Total distance covered in the second time would be (140+x+8)km

________________________________

Time For First Distance

↪Time taken to cover 140km by the speed of 6 km/hr = 140/6 or 23.34 hours

↪Time taken to cover xkm by the speed of 10km/hr = x/10 __________(EQ.1)

↪Total time taken to cover the first distances is (23.34+x/10) hours

________________________________

Time For Second Distance

↪Time taken to cover 140 km by the speed of 10km/hr = 140/10 or 14 hours

↪Time taken to cover xkm by the speed of 6km/hr = x/6 ______(EQ.2)

↪Time taken to cover 8 km by the speed of 60km/hr = 8/6 or 1.34 hours

↪Total time taken to cover the second distances is (14+1.34+x/6) hours or (15.34+x/6) hours

_______________________________

As, we know the time taken by covering both distance is same, we can say that -

➠Total time taken to cover the first distance = Total time taken to cover the second distance

➠23.34 + x/10 = 15.34 + x/6

➠ x/6 - x/10 = 23.34-15.34

➠ (10x-6x)/60 = 8

➠x = 480/4

➠x = 120 km

so, the remaining distance must be 120 kilometres

_______________________________

Now,

putting the values in equation 1

⇝120/10 = 12 hours

⇝Total time taken to cover first distance = (23.34+12)hours or 35.34 hours _____(EQ.3)

_______________________________

Now,

putting the values in equation 2

⇝120/6 hours = 20 hours

⇝Total time taken to cover second distance = (14+1.34+20) hours or 35.34 hours ______(EQ.4)

so, from equations 3 & 4 we can conclude that time taken to cover both distances are same i.e., 35.34 hours

_______________________________

Total Distance = 260 kms

⟹ Average speed = Total Distance/Total time

⟹ Average speed = 260/35.34 or 7.35 kilometres

_______________________________

Now,

↪Total time taken to cover 140 kilometres at an average speed = 140/7.35 or 19.04

_______________________________