Ques: A car going at 40 miles per hour set out on an 80-mile trip at 9:00 A.M. Exactly 10 minutes later, a second car left from the same place and followed the same route. How fast, in miles per hour, was the second car going if it caught up with the first car at 10:30 A.M.?

I am trying to solve the problem using relative speed, Greg has solved it using relative speed along with answer choices, how do I solve it without answer choice, what mistake I am making here?

d= 80Miles, ra= 40MPH, @10.30AM, d= 60 Miles

@10 minutes, d= 40/60 *10 =20/3

d= 60-20/3 = 160/3

160/3=(rb-40) x 80Minutes

160/240= rb-40

2/3+40=rb

rb=122Mile/3Minute

Thank you.

What you can do is, interpret that the 2nd car is faster than the 1st one.

So, after leaving 10 minutes late, it will have 80 minutes to catch up with the 1st car.

So, the 2nd car is going to cover the same distance in 80 mins. Which means, that the distance to cover is 60 miles.

Hence, the 2nd car has to cover 60 miles in 80 minutes.

Convert the minutes to hours and calculate the rate as 60 miles / (80/60) hours = 45 miles/hour.

(Correct me if I’m wrong )

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Why would 2nd car cover 60 miles, shouldn’t it cover,

d= 60-20/3 = 160/3 miles, as for the first 10 minutes it has already covered 20/3 miles which should be deducted from 60 miles.

What is it I am getting wrong here?

Thank you.

I’d suggest you to rather visualize the whole scene first. As for the question explicitly says that the car left after 10 minutes from the same place, meaning the initial place which means in less time the 2nd car has to cover the same distance, that is 60 miles.

Thank you @sherlockthebond . Understood it correctly now.

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