Question

Ravi rode a bike at a speed of 45km/h to cover a certain distance. Amrit covered 30 km more than Ravi did. Amrit took 2 hours more than Ravi to reach his destination at a-speed of 30 km/hr. Find the distance each person covered.​

Answer 1

Step-by-step explanation:

Let the distance traveled by Ravi to reach his destination be : R km

Given : Ravi rode his bike at a speed of 45 km/hr

It means : In one hour Ravi travels a distance of 45 km

$\bigstar\;\;\textsf{We know that : \boxed{\mathsf{Speed = \dfrac{Distance\;traveled}{Time\;taken}}}}$

$\implies \mathsf{Time\;taken = \dfrac{Distance\;traveled}{Speed}}$

$\implies \mathsf{Time\;taken\;by\;Ravi\;to\;cover\;R\;km\;will\;be : \dfrac{R}{45}\;hours}$

Given : Amrit covered 30 km more than the distance Ravi covered

$\longrightarrow$  Total distance traveled by Amrit = (R + 30)

Given : Amrit rode his bike at a speed of 30 km/hr

$\implies \mathsf{Time\;taken\;by\;Amrit\;to\;cover\;(R + 30)\;km\;will\;be : \dfrac{R + 30}{30}\;hours}$

Given : Amrit took 2 hours more than Ravi to reach his destination

$\implies \mathsf{\dfrac{R + 30}{30} - 2 = \dfrac{R}{45}}$

$\implies \mathsf{\dfrac{R}{30} + 1 - 2 = \dfrac{R}{45}}$

$\implies \mathsf{\dfrac{R}{30} - 1 = \dfrac{R}{45}}$

$\implies \mathsf{\dfrac{R - 30}{30} = \dfrac{R}{45}}$

$\implies \mathsf{45(R - 30) = 30R}$

$\implies \mathsf{45R - 30R = 1350}$

$\implies \mathsf{15R = 1350}$

$\implies \mathsf{R = 90}$

$\implies \textsf{Distance traveled by Ravi to reach his destination = 90 km}$

$\implies \textsf{Distance traveled by Amrit to reach his destination = 120 km}$