Question

reeta travels a distance of 370km partly by bus and partly by car when she travels 250 km by bus and rest by car takes 8 hours to reach her destination if she travels 200km by bus and rest by car take 15 minutes longer find the speed of the bus and car.​

Answer 1

$\large\underline{\sf{Solution-}}$

Let us assume that speed of the bus be x km/ hr and speed of car be y km/ hr.

Case :- 1

Total distance = 370 km

Distance travelled by bus = 250 km

So,

Distance travelled by car = 120 km

Total time taken to travel 370 km = 8 hours.

We know,

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

Hence,

$\rm :\longmapsto\:\dfrac{250}{x} + \dfrac{120}{y} = 8 - - - (1)$

Case :- 2

Total distance = 370 km

Distance travelled by bus = 200 km

So,

Distance travelled by car = 170 km

Total time taken to travel 370 km = 8 hours 15 min.

Hence,

Now, we have two equations

$\rm :\longmapsto\:\dfrac{250}{x} + \dfrac{120}{y} = 8 - - - (1)$

and

$\rm :\longmapsto\:\dfrac{200}{x} + \dfrac{170}{y} =\dfrac{33}{4} - - - (2)$

Let assume that,

$\red{\rm :\longmapsto\:\dfrac{1}{x} = u}$

and

$\red{\rm :\longmapsto\:\dfrac{1}{y} = v}$

So, equation (1) and (2) reduces to

$\rm :\longmapsto\:250u + 120v = 8 - - - (3)$

and

$\rm :\longmapsto\:200u + 170v = \dfrac{33}{4} - - - (4)$

Now, multiply equation (3) by 4 and equation (4) by 5, we get

$\rm :\longmapsto\:1000u + 480v = 32 - - - (5)$

and

$\rm :\longmapsto\:1000u + 850v = \dfrac{165}{4} - - - (6)$

On Subtracting equation (5) from equation (6), we get

$\rm :\longmapsto\:370v = \dfrac{37}{4}$

$\rm :\longmapsto\:v = \dfrac{1}{40}$

On substituting the value of v in equation (4), we get

$\rm :\longmapsto\:200u + 170 \times \dfrac{1}{40} = \dfrac{33}{4}$

$\rm :\longmapsto\:200u + \dfrac{17}{4} = \dfrac{33}{4}$

$\rm :\longmapsto\:200u = \dfrac{16}{4}$

$\rm :\longmapsto\:200u = 4$

$\rm :\longmapsto\:u = \dfrac{1}{50}$

Hence,

$\rm :\longmapsto\:x = 50 \: km \: per \: hour$

and

$\rm :\longmapsto\:y = 40 \: km \: per \: hour$