SOLUTION: Aaron left L.A. to drive at 55 mph towards Las Vegas. Mike left L.A. an hour after Aaron (also towards Las Vegas), driving at 70 mph. How long will it take Mike to overtake Aaron?

Question 1205635: Aaron left L.A. to drive at 55 mph towards Las Vegas. Mike left L.A. an hour after Aaron (also towards Las Vegas), driving at 70 mph. How long will it take Mike to overtake Aaron?
Found 2 solutions by Theo, greenestamps:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
mike will catch up to aaron when they have both traveled the same distance.
mike will have been on the road 1 hour less than aaron because he started an hour later.

rate * time distance is the basic formula used.

for aaron, you get r * t = d
r is the rate
t is the time in hours
d is the distance in miles.

for mike, you get r * (t-1) = d
r is the rqte
t-1 is the time in hours.
d is the distance in miles.

these these two equations need to be solved simultaneously.

for aaron, the equation becomes 55 * t = d
for mike, the equation becomes 70 * (t-1) = d

since they are both equal to d, you can set 55 * t equal to 70 * (t-1)
simplify to get 55 * t = 70 * t - 70
subtract 55 * t from both sides of the equation and add 70 to both sides of the equation to get 70 = 15 * t
solve for t to get t = 4.66666666.....

aaron's equation becomes 55 * 4.6666666.... = d
mike's equation becomes 70 * 3.6666666.... = d

solve for d to get d = 256.666666.... in both equations.

your solution is that mike will overtake aaron in 3 and 2/3 hours.

Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

In the hour that Aaron travels at 55mph before Mike starts driving, he travels 55 miles.

The rate at which Mike catches up to Aaron is the difference of their speeds, which is 70-55 = 15mph.

The number of hours it takes Mike to catch up to Aaron is 55/15 = 11/3 hours.

ANSWER: 11/3 hours, or 3 2/3 hours, or 3 hours 40 minutes

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