A planehas 7 hrs. to reach a target and come back to base. it flies out to the target at 480 miles per hr. and returns on the same route at 640 miles per hour. how many miles from the base is the target?
let the time for the "out-trip" be t hours
then the return trip took 7-t hours
so first distance = 480t miles
return distance = 640(7-t)miles
but aren't the two distances equal ?
so solve
480t = (640(7-t)
then sub your value of t into 480t
To find the distance from the base to the target, we can use the formula:
Distance = Speed * Time
Let's consider the outbound trip first. The plane flies at a speed of 480 miles per hour for a total time of 7 hours. Therefore, the distance covered during the outbound trip is:
Distance_outbound = 480 miles/hour * 7 hours = 3360 miles
Now, let's consider the return trip. The plane flies at a speed of 640 miles per hour for a total time of 7 hours. Therefore, the distance covered during the return trip is:
Distance_return = 640 miles/hour * 7 hours = 4480 miles
Since the outbound and return trips cover the same distance, we can equate the distances:
Distance_outbound = Distance_return
3360 miles = 4480 miles
Now, to find the distance from the base to the target, we'll calculate half of the total distance:
Distance_target = Distance_outbound / 2
Distance_target = 3360 miles / 2 = 1680 miles
Therefore, the target is located 1680 miles from the base.