your aunt and uncle have been visiting at your home. five minutes after they drive away, you realize that they forgot their luggage. you happen to know that they drive slowly, so you get in your car and drive to catch up with them. your average speed is 10 miles an hour faster that their average speed, and you catch up with them in 25 minutes. how fast did you drive?

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jaiswaljyoti jaiswaljyoti · Answer 1 · 2022-12-21T12:38:58+01:00

Since, We catch the other car if our speed of our car is 60mph.

When you catch up, the distance traveled is the same

Let us consider x as the velocity.

Therefore, our velocity is x + 10

We know that:

Distance = rate x time

According to the question:

r = uncle's rate

30 min = 30/60 hr = uncle's time

25 min = 25/60 hr = your time

and

Uncle's distance = Your distance

Now,

(r)(30/60) = (r + 10)(25/60)

⇒ (r)(1/2) = (r + 10)(5/12)

⇒ r/2 = 5r/12 + 50/12

⇒ 6r = 5r + 50

⇒ r = 50

Now,

Uncle's rate = 50 mph

and, putting the values:

Your rate = 50 + 10 = 60 mph

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