Question

Ravi rode his bike at a speed of 45 km/hr to cover a certain distance. Amrit covered
30 km more than the distance Ravi covered, 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

Let Ravi covered x km.

and time taken to cover the distance be y hours. At 45km/hr.

Amrit covered (x +30) km.

and time taken (y +2) hours. At 30km/hr.

By given condition,

Ravi , x÷y = 45 ...( Distance formula )

by cross multiplication,

°° x= 45 × y

°° x - 45y = 0 ... ( 1 )

Amrit, x + 30 ÷ y + 2 = 30 ...( Distance formula )

cross multiplication,

x + 30 = (y+2) ×30

x + 30 = 30y + 60

x - 30y = 60 - 30

x - 30y = 30 ...(2)

subtract eq`n (1) from (2)

x - 30y = 30 ...(2)

-x -(-45y)= 0 ...(1)

_________

15y = 30

{ y = 2 } ...

•°• Ravi takes 2 hours to complete

•°• Amrit takes ( y + 2 ) = 4 hours to complete

Ravi { x ÷ y = 45 } ...( Distance formula )

•°• x ÷ 2 = 45 ...{ putting (y = 2)}

x = 90 km

•°• Ravi covered = 90km

•°• Amrit covered = (x + 30)km = ( 90 + 30 ) = 120 km..

Justify Answer☺☺☺

Answer 2

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

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

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

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

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

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

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

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

$\implies \mathsf{R = 90}$

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

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