Question

There are two friends A and B. A starts with his car at the speed 40 kmph. B starts one hour later from the same place, in the same direction on his bike at the speed of 50 kmph. After how many hours will they meet

Answer 1

Given :  There are two friends A and B. A starts with his car at the speed 40 kmph. B starts one hour later from the same place, in the same direction on his bike at the speed of 50 kmph.

To Find : After how many hours will they meet

Solution:

Let say they meet after T hours from when A starts

Speed of A = 40 km/hr

Time = T hrs

Distance = Speed x Time

=> Distance = 40T  km

Speed of B = 50 km/hr

B starts after 1 hr

Time = T-1  hrs

=> Distance = 50(T-1)  km

40T = 50(T-1)

=> 4T = 5(T - 1)

=> 4T = 5T - 5

=> T = 5

After 5 hrs from when A starts and after 4 hrs from when B starts

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Answer 2

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

FORMULA TO BE IMPLEMENTED

For a moving body traveling a distance

$\displaystyle \: \sf{ \: Time \: required = \frac{ Distance \: covered }{Speed \: of \: the \: body \: } \: }$

GIVEN

There are two friends A and B. A starts with his car at the speed 40 kmph. B starts one hour later from the same place, in the same direction on his bike at the speed of 50 kmph

TO DETERMINE

The time after which they will meet

CALCULATION

Let at a distance of x km from starting point they will meet

The speed of A & B is 40 kmph & 50 kmph respectively

So the time required for A to travel the distance of x km is

$= \displaystyle \: \sf{ \: \frac{x}{40} \: } \: hour$

So the time required for B to travel the distance of x km is

$= \displaystyle \: \sf{ \: \frac{x}{50} \: } \: hour$

By the given condition

$\displaystyle \: \sf{ \: \frac{x}{40} \: - \frac{x}{50} = 1 }$

$\implies \: \displaystyle \: \sf{ \: \frac{5x - 4x}{200} \: = 1 }$

$\implies \: \displaystyle \: \sf{ \: \frac{x }{200} \: = 1 }$

$\implies \: \displaystyle \: \sf{ \: x \: = 200 }$

So the time required for A to travel the distance of 200 km is

$= \displaystyle \: \sf{ \: \frac{200}{40} \: } \: hour = 5 \: \: hour$

So the time required for B to travel the distance of 200 km is

$= \displaystyle \: \sf{ \: \frac{200}{50} \: } \: hour = 4\: \: hour$

Hence after 5 hours from starting of A & after 4 hours of starting of B the two friends A & B will meet

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