SOLUTION: A jogger started a course at 4.5 mph. A cyclist started the same course 1 hour later at an average speed of 14 mph. How long after the jogger started did the cyclist take over th

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Question 282321: A jogger started a course at 4.5 mph. A cyclist started the same course 1 hour later at an average speed of 14 mph. How long after the jogger started did the cyclist take over the jogger? Round to the nearest tenth of an hour.
Found 4 solutions by mananth, ikleyn, josgarithmetic, greenestamps:
Answer by mananth(16949)   (Show Source):
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A jogger started a course at 4.5 mph. A cyclist started the same course 1 hour later at an average speed of 14 mph. How long after the jogger started did the cyclist take over the jogger? Round to the nearest tenth of an hour.
let the cyclist meet the jogger at a distance x from the start
He starts after 1 hour after the jogger starts
so jogger would have traveled 4.5 miles by that time.
distance traveled by jogger when cyclist meets him will be x-4.5 miles
the time they travel after cyclist starts is the same.
time taken by jogger = x-4.5 / 4.5
time taken by cyclist = x/14

x/14 = x-4.5 /4.5
4.5x/14 = x-4.5
4.5x = 14(x-4.5)
4.5x= 14x- 63
-9.5x=-63
x= -63/-9.5
x=6.6 miles the distance they meet from the start
Time taken by jogger to jog (6.6-4.5) = 2.1 miles = 2.1/4.5= 0.46 hours
the cyclist meets the jogger after 1.46 hours after the jogger started

Answer by ikleyn(53742)   (Show Source):
You can put this solution on YOUR website!
.
A jogger started a course at 4.5 mph. A cyclist started the same course 1 hour later at an average speed of 14 mph.
How long after the jogger started did the cyclist take over the jogger? Round to the nearest tenth of an hour.
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        Calculations and the answer in the post by @mananth are not accurate
        I came to bring a correct solution.

When the cyclist starts, the jogger is 4.5 miles ahead. The rate of approaching is 14 - 4.5 = 9.5 miles per hour. Therefore, the time when the cyclist will take over the jogger is = = = 0.474 of an hour, or 28.42 minutes after the cyclist' start. The distance from the start to the catching point is , which is about 6.632 mile. ANSWER. The time when the cyclist will take over the jogger is 0.474 of an hour, or 28.42 minutes. The distance from the start to the catching point is about 6.632 mile.

Solved correctly.

Answer by josgarithmetic(39790)   (Show Source):
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SPEED TIME DISTANCE JOGGER 4.5 t 4.5t CYCLIST 14 t-1 14(t-1)

1 hour 28 minutes

The cyclist needed 28 minutes (and a few more seconds) to catchup.

Answer by greenestamps(13326)   (Show Source):
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When the cyclist starts, the jogger has been running for an hour at 4.5 mph, covering a distance of 4.5 miles.

The rate at which the cyclist catches up to the jogger is the difference in their rates, which is 14-4.5 = 9.5 mph.

The time required for the cyclist to catch up to the jogger is the catch-up distance divided by catch-up the rate, which is 4.5/9.5 = 9/19 hours.

The question asks for the time after the jogger starts for the cyclist to catch up to the jogger; that is 1 + 9/19 = 28/19 hours.

28/19 = 1.4736...

Rounded to the nearest tenth of an hour, per the instructions...

ANSWER: 1.5 hours