A refrigerated truck leaves a rest stop traveling at a steady rate of 56 mi/h. A car leaves the same rest stop 1/4 hours later following the truck at a steady rate of 64 mi/h. How long after the truck leaves the rest stop will the ca overtake the truck?
To find out how long after the truck leaves the rest stop will the car overtake the truck, we need to determine the time it takes for the car to catch up with the truck.
Let's assume that the car will overtake the truck after t hours.
In that case, during t hours, the truck would have traveled a distance of 56t miles, and the car would have traveled a distance of 64(t - 1/4) miles.
Since the car catches up with the truck, their distances traveled will be the same:
56t = 64(t - 1/4)
Solving this equation will give us the value of t.
Expand the equation:
56t = 64t - 16
Combine like terms:
64t - 56t = 16
8t = 16
Divide both sides by 8:
t = 16/8
t = 2
Therefore, it will take the car 2 hours to overtake the truck after the truck leaves the rest stop.
To solve this problem, we need to find the time it takes for the car to catch up to the truck. This can be done by setting up an equation using the information given.
Let's assume the car overtakes the truck after t hours.
For the truck:
Distance traveled by the truck = Rate of the truck * Time taken by the truck
For the car:
Distance traveled by the car = Rate of the car * Time taken by the car
Given that the car leaves the rest stop 1/4 hours later than the truck, we can say the car has less time to travel the same distance as the truck. Therefore, the time taken by the car is t - 1/4 hours.
Now, equating the distances traveled by the car and the truck:
Rate of the truck * Time taken by the truck = Rate of the car * Time taken by the car
56 * t = 64 * (t - 1/4)
To solve for t, we can simplify the equation:
56t = 64t - 16
Rearrange the equation:
64t - 56t = 16
8t = 16
Divide both sides by 8:
t = 16/8
t = 2
Therefore, it will take the car 2 hours to overtake the truck after the truck leaves the rest stop.
When the car starts, the truck is 56/4 = 14 miles ahead.
the car is going 8 mi/hr faster.
So, how long will it take to make up the 14 miles?
Add that to the 1/4 hr the truck already traveled.