Distance = Rate x Time word problem

dboybbfs

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Have to do this in graph formation. This is what I came up with: Distance for both are 30. Rate for cyclist is 2x. Rate for the jogger is x. Don't know where time fits into equation though. The only formula I could come up with was 30/2x = 30/x but that doesn't work out.

thanks

Problem:

A cyclist and a jogger both leave san antonio at 6:00 pm heading to the supermarket, which is 30 miles away. The cyclist is traveling twice as fast as the jogger and arrives at the supermarket three hours before the jogger. Find the cyclist's speed.
 
dboybbfs said:
Have to do this in graph formation. This is what I came up with: Distance for both are 30. Rate for cyclist is 2x. Rate for the jogger is x. Don't know where time fits into equation though. The only formula I could come up with was 30/2x = 30/x but that doesn't work out.
Problem:
A cyclist and a jogger both leave san antonio at 6:00 pm heading to the supermarket, which is 30 miles away. The cyclist is traveling twice as fast as the jogger and arrives at the supermarket three hours before the jogger. Find the cyclist's speed.
time by jogger = t ; so time by cyclist = t-3

x = 30/t

2x = 30/(t-3)

Finish it.
 
dboybbfs said:
Have to do this in graph formation. This is what I came up with: Distance for both are 30. Rate for cyclist is 2x. Rate for the jogger is x. Don't know where time fits into equation though. The only formula I could come up with was 30/2x = 30/x but that doesn't work out.

thanks

Problem:

A cyclist and a jogger both leave san antonio at 6:00 pm heading to the supermarket, which is 30 miles away. The cyclist is traveling twice as fast as the jogger and arrives at the supermarket three hours before the jogger. Find the cyclist's speed.

Here's a slightly different approach.

What do your expressions of 30/2x and 30/x represent?

Distance = rate * time
Distance/rate = time

2x is the speed for the cyclist, and 30 is the distance, so 30/(2x) is the TIME it takes the cyclist to make the trip.

x is the speed of the jogger, and again 30 is the distance, so 30/x is the TIME it takes the jogger to make the trip.

What do we know?

Time for cyclist is 3 hours less than time for jogger
30/(2x) = (30/x) - 3

Now, multiply both sides of the equation by the LCD of the fractions, and solve for x. Remember that you are asked for the speed of the cyclist, so your "final answer" will be the value of 2x.
 
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