Question

Two cars are traveling north along a highway. The first drives at 40 mph, and the second, which leaves 3 hours later, travels at 60 mph. How long after the second car leaves will it take for the second car to catch the first?

Answer 1

Step-by-step explanation:

• Let both the cars meet after a hours after the first car starts.
• So at the rate of 40 m/hr the first car travels.
• So the first car travels at a distance of 40 a
• So at the rate of 60 m/hr the second car travels.
• Now the time taken by 2nd car to catch up is (a – 3) (since it starts 3 hrs late)
• So distance travelled by 2nd car is 60(a – 3)
• Equating both we get  40 a = 60 (a – 3)
•  Simplifying the equation we get 40 a = 60 a – 180
•                         20 a = 180
•                           Or a = 9 hrs.
• Now after second car starts the time taken  will be 9 – 3 = 6 hrs

Reference link will be

https://brainly.in/question/24091013?

Answer 2

Answer:

The second car will take 6 hours to catch the first car, after the second car leaves.

Step-by-step explanation:

Consider that T is the time when second car will catch the first car.

Distance travelled = speed× Time

Given, the speed of the first car = 40mph

First car leaves 3 hours before the second car,

Distance travelled by first car in time (T+3 )= (40)(T+3)               ............(1)

The speed of second car = 60mph

Distance travelled by 2nd car in time (T)$=(60)(T)$                       ...........(2)

When second car will catch the first car, the distance travelled by both cars will be same.

So, compare the equation (1) with eq.(2):

$40(T+3)=60(T)$

$40T+120=60T$

$60T-40T=120$

$20T=120$

$T=6\; hours$

Therefore, the second car will catch the first car after 6 hours.