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.