SOLUTION: A motorcycle traveling at 70 miles per hour overtakes a car traveling at 40 miles per hour that had a three- hour head start. How far from the starting point are the two vechicles

Question 217867: A motorcycle traveling at 70 miles per hour overtakes a car traveling at 40 miles per hour that had a three- hour head start. How far from the starting point are the two vechicles.

Found 2 solutions by Alan3354, MathTherapy:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
A motorcycle traveling at 70 miles per hour overtakes a car traveling at 40 miles per hour that had a three- hour head start. How far from the starting point are the two vechicles.
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The car is 120 miles away when the motorcycle starts.
The bike gains on the car at 30 mph (70-40).
It take 4 hours for the bike to close the gap (120/30).
In 4 hours, the bike and the car are 280 miles from the starting point.
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4*70 = 280
7*40 = 280

Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!
A motorcycle traveling at 70 miles per hour overtakes a car traveling at 40 miles per hour that had a three- hour head start. How far from the starting point are the two vechicles.

Let the time that the faster vehicle (motorcycle) takes to get to the meeting point be T

Then the time that the car takes to get to the meeting point is T + 3 since it had a 3-hour head start, and is the slower vehicle

Since Distance = Speed x Time, and in this case the distances are equal, we therefore have: 70T = 40(T + 3)

70T = 40T + 120

30T = 120

, which makes the distance that both vehicles traveled, miles, calculated as (70 * 4), or (40 * 7).

It also means that the motorcycle took 4 hours to travel 280 miles, and the car took 3 hours more, or 7 hours to travel the same distance.
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