Two truck drivers leave the same rest stop at the same time to travel in opposite directions.One travel at an average rate of 52 mph and the other average 56 mph.In how many hours will they be 72 miles apart
let the time be t hrs
52t + 56t = 72
take over to solve for t
(hint: it will clearly be less than 1 hr)
To find the number of hours it will take for the two trucks to be 72 miles apart, we can use the concept of relative motion. We know the average rates at which the trucks are traveling in opposite directions: one at 52 mph and the other at 56 mph.
Relative motion is the combined effect of the individual motions of two objects moving in opposite directions. In this case, the trucks are moving away from each other, so we need to consider their combined speed. To find the relative speed, we add the speeds of the two trucks:
Relative speed = Speed of Truck 1 + Speed of Truck 2
Relative speed = 52 mph + 56 mph
Relative speed = 108 mph
Now we can calculate the time it will take for the trucks to be 72 miles apart using the formula:
Time = Distance / Speed
Time = 72 miles / 108 mph
Time = 2/3 hours or 40 minutes
Therefore, it will take 40 minutes for the two trucks to be 72 miles apart.