Question

1.The distance from A to B by two different routes are 75km
and 77 km. A car taking the longer route travels on an
average 6km/h faster than the one that takes shorter route
and completes the journey in 15 min less time. Find the
speed of each car.

Answer 1

Speed of car taking the shorter route = 36 km/h

Speed of car taking longer route = 42 km/h

Step-by-step explanation:

Here we will use the formula

Distance = Speed × Time

Let the car taking the shorter route (75 km) has velocity = v km/h

Then the velocity of the car taking longer route (77 km) = (v+6) km/h

According to the question

$\frac{75}{v}-\frac{77}{v+6}=\frac{15}{60}$

$\implies 75(v+6)-77v=\frac{v(v+6)}{4}$

$\implies (-2v+75\times 6)\times 4=v^2+6v$

$\implies -8v+1800=v^2+6v$

$\implies v^2+14v-1800=0$

$\implies v^2+50v-36v-1800=0$

$\implies v(v+50)-36(v+50)=0$

$\implies (v-36)(v+50)=0$

$\implies v=36,-50$

But speed can't be negative

Therefore, $v=36$ km/h

Therefore, the speed of car taking the shorter route = 36 km/h

Speed of car taking longer route = 36+6=42 km/h

Hope this answer is helpful.

Know More:

Q: A person travelled 270 km by car, 450 km by train and 120 km by bus. it took 15.5 hours . if the speed of car is 4/5 times the speed of train and 2.5 times the speed of bus. what is the speed of car?

Click Here: https://brainly.in/question/2292490

Answer 2

Answer:

Speed of car taking the shorter route = 36 km/h

Speed of car taking longer route = 42 km/h

Step-by-step explanation:

Here we will use the formula

Distance = Speed × Time

Let the car taking the shorter route (75 km) has velocity = v km/h

Then the velocity of the car taking longer route (77 km) = (v+6) km/h

According to the question

But speed can't be negative

Therefore,  km/h

Therefore, the speed of car taking the shorter route = 36 km/h

Speed of car taking longer route = 36+6=42 km/h

Hope this answer is helpful.