SOLUTION: A bicyclist biking on a straight road at a steady 12 mph is being chased by a dog running at 15 miles per hour. if the cyclist is 50ft ahead of the dog and each continues at the sa

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Question 320965: A bicyclist biking on a straight road at a steady 12 mph is being chased by a dog running at 15 miles per hour. if the cyclist is 50ft ahead of the dog and each continues at the same rate, how long, to the nearest 10th of a minute, will it take the dog to catch up to the cyclist?
please state what each variable you used to represents
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A bicyclist biking on a straight road at a steady 12 mph is being chased by a dog running at 15 miles per hour.
if the cyclist is 50ft ahead of the dog and each continues at the same rate,
how long, to the nearest 10th of a minute, will it take the dog to catch up to the cyclist?
:
Since the speed is in mph and the distance between them is in feet convert both
the cyclist speed and the dog's speed to ft/min
:
Dog:%2815%2A5280%29%2F60 = 1320 ft/min
and
Cyclist:%2812%2A5280%29%2F60 = 1056 ft/min
:
Let t = time in min for dog to catch bike
:
Write a simple distance equation, Dist = speed * time
:
dog dist - 50 ft = cyclist dist
1320t - 50 = 1056t
1320t - 1056t = 50
264t = 50
t = 50%2F264
t = .189 ~ .2 min for the dog to catch the bike, (about 12 seconds)
:
:
Check solution by finding the distance traveled by each
.189(1320) = 249.5 ft (dog)
.189(1056) = 199.5 ft (bike)
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difference of 50 ft