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Question

In a bike race Josh gives Rob a 500 meter advantage. Also josh agrees to start the race 15 minutes after rob.If josh bikes at 17KM/hour and Rob at 14 Km/hour, how long will it take josh to overtake rob?

I dont know how to set this problem up

Answer 1

I cant either i never got past that frog story problem.

Answer 2

Josh bikes 3 km/h faster than Rob.

In the first 15 minutes Rob bikes 14/4 km or 3.5 km.

He also has the 500 m advantage so is 4 km ahead of Josh.

So the question is how long will it take Josh to make up for the 4 km lead that Rob has.  

It will take Josh 4/3 hours after he starts or 80 minutes. (80 minutes after Josh starts, 95 minutes after Rob).

Answer 3

First you could set up a coordinates for a graph of there speeds.

Rob at 14km/hour would have the equation d = h*14 (distance equals hour times 14). So this would be his coordinates.

0 - 0

1 - 14

2 - 28

3 - 42

4 - 56

5 - 70

Josh would have a bit more complicated graph though since he is waiting at the start line while time goes. His graph would be d = (h-.25)*17 - .5 ----> In other words this equation for his coordinates (place in the race) shows that he goes 17 kilometers ever 1.25 hours because he never actually got going until .25 hours so it wasn't until 1.25 hours that he had gone 17 kilometers and then you must also take away .5 km's since he also didn't start until 500 meters or .5 kilometers after the 1.25 hour time period. After all of that you get how far he has actually gotten since Rob started the timer. So here is Josh's coordinate's.

0 - 0

1 - 12.25

2 - 29.25

3 - 46.25

4 - 63.25

From this you can tell that when Rob hit the two hour point he had only gone 28 kilometers while Josh had gone 29.25 so it was at sometime before 2 hours that Josh had to have passed up Rob. If you plug those two equations into a graphing calculator as y=x*14 and y=(x-.25)*17-.5 then you can find out that the lines intersect at x=1.58333 and y=22.1666 or in other words after 1 hour and 35 minutes they both were tied with eachother at 22 kilometers and 166&two-thirds meters so immediately after that Josh passed up Rob.

In Short: 1 Hour 35 Minutes and 22 Kilometers 166&two-thirds meters