A train travels at 80 mph and a bicycle at 10 mph. If they start 4 hours apart, when will the bicycle catch up?
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To solve this problem, we can set up an equation based on the fact that distance equals rate multiplied by time (d = rt).
Let's assume that the time it takes for the bicycle to catch up to the train is t hours.
When the bicycle starts, the train has already been traveling for 4 hours. So, the time the train has been traveling is t + 4 hours.
The distance traveled by the bicycle is equal to the distance traveled by the train when they meet.
Distance covered by the bicycle = Distance covered by the train
Using the formula d = rt, we can set up the equation:
10t (distance covered by the bicycle) = 80(t + 4) (distance covered by the train)
Now, we can solve for t:
10t = 80t + 320
Subtract 80t from both sides:
-70t = 320
Divide by -70:
t = -320/70
t ≈ -4.57
Since time cannot be negative, we can disregard the negative value.
Therefore, the bicycle catches up to the train at approximately 4.57 hours after it starts.
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