Question

Question:-
Two cyclists make the same trip. The first one take 3.5 hours and the second ,with a speed that is 1km/h greater than that of the first ,take 3 hours.find the speed of the two cyclists.also find the distance covered in the trip.
​

Answer 1

$\huge\boxed{\underline{\sf{\red{ᴀ}\green{ɴ}\pink{s}\orange{ᴡ}\blue{ᴇ}\pink{ʀ}}}}$

Question:-

Two cyclists make the same trip. The first one take 3.5 hours and the second ,with a speed that is 1km/h greater than that of the first ,take 3 hours.find the speed of the two cyclists.also find the distance covered in the trip.

Given:-

Two cyclists make the same trip.

Time Taken by first cyclist = 3.5 hrs

Time Taken by second cyclist = 3 hrs

To Find:-

speed of the two cyclists.

distance covered in the trip.

Solution:-

Let the speed of first cyclist be x

Time taken by the first cyclist = 3.5 hours

Distance Travelled by first cyclist

⇒speed × time

⇒ 3.5x

We are given that the second with a speed that that is 1 km/h greater than that of the first, takes 3 hours .

So,

The speed of the second cyclist = x + 1

Time Taken by second cyclist = 3 hours

Distance Travelled by second cyclist

⇒Speed × Time

⇒ 3(x + 1)

Since we are given that cyclist travelled the same time

So,

3.5x = 3(x + 1)

3.5x = 3x + 3

0.5 x = 3

x = 3/0.5

x = 6

Distance Travelled by the first cyclist

⇒ 3.5x = 3.5(6)

⇒ 21

Hence, The distance covered in the trip is 21km

━━━━━━━━━━━━━━━━━━━━━━━━━

Answer 2

Given :-

Time taken by the first cyclist = 3.5 hours

Time taken by the second cyclist = 3 hours

Speed of the second cyclist = 1 km/h greater than the first cyclist

To Find :-

The speed of the two cyclist.

The distance covered in the trip.

Solution :-

Assume that,

Speed of the first cyclist (s₁) = x

Speed of the second cyclist (s₂)  = x + 1

According to the question,

$\underline{\boxed{\sf Speed \times Time = Speed \times Time}}$

Given that,

Speed (s₁) = x km/h

Time (t₁) = 3.5 hours

Speed (s₂) = x + 1 km/h

Time (t₂) = 3 hours

Substituting their values,

⇒ x × 3.5 = x + 1 × 3

⇒ 3.5x = 3(x + 1)

⇒ 3.5x = 3x + 3

⇒ 3 = 3.5x - 3x

⇒ 3 = 0.5x

⇒ x = 3/0.5

⇒ x = 6

Finding the speed,

Speed of the first cyclist = 6 km/h

Speed of the second cyclist = x + 1 = 7 km/h

Finding the distance covered,

Distance covered = x × 3.5

⇒ 6 × 3.5

⇒ 21 km

Therefore, the distance covered in the trip is 21 km.