Can someone help me with this math word problem please?

Question

Two planes, which are 3780 miles apart, fly toward each other. Their speeds differ by 45MPH. If they pass each other in 4 hours, what is the speed of each?

Answer 1

Use the distance equation D = RT

Let the speed of the slower plane be R(1). Then it travels a distance, D(1) = R(1)T, in 4 hours.

Let the speed of the faster plane be R(2) = R(1) + 45 mi/hr, because it is traveling 45 mi/hr faster than the other plane. Then it travels a distance, D(2) = R(2)T = [R(1) + 45 mi/hr]T, in 4 hours.

You know D(1) + D(2) = D(total) = 3780 mi. We also know that T = 4 hr. So now all we have to do is add the equations for the distances traveled by the planes individually and solve for R(1). Then we add 45 mi/hr to that and we are finished.

D(total) = D(1) + D(2) = R(1)T + [R(1) + 45 mi/hr]T = 3780 mi
D(total) = R(1)T + R(1)T + (45 mi/hr)T = 3780 mi
D(total) = 2R(1)T + (45 mi/hr)T
3780 mi = 4 hr [2R(1)] + 4 hr (45 mi/hr)
3780 mi = 8 hr [R(1)] + 180 mi
(3780 mi - 180 mi) = 8 hr [R(1)]
3600 mi/8 hr = R(1)
(3600/8) mi/hr = R(1)
450 mi/hr = R(1)

450 mi/hr + 45 mi/hr = R(2)
495 mi/hr = R(2)

So the planes are traveling at 450 mi/hr and 495 mi/hr respectively.

As a check, substitute the final results into the equation D(total) = R(1)T + R(2)T. If D(total) = 3780 mi, then our solution is correct.

D(total) = 4 hr (450 mi/hr) + 4 hr (495 mi/hr)
D(total) = 1800 mi + 1980 mi
D(total) = 3780 mi

Our answer is correct!

Answer 2

This is how I would solve it.

1. You have to consider that if they are passing each other, that they both only went HALF of the distance of the total 3780 miles (so take 3780/2).

2. Then, they both took that half-distance in 4 hours (so the answer from #1/4)

3. THEN, knowing their speeds differed by 45mph, but also knowing that adding 45 to one plane and subtracting it from the other would make their speeds differ by 90, you have to find the half of 45mph (so, 45/2)

4. Add the half of 45 to one plane speed found and subtract it from the other. This will give you the speed of each plane. (the answer, in other words, to the problem)

**To double-check your work on this, take each speed answer times the 4 hours it took them to travel the distance to meet each other. Then add the two totals, and if you come up with the original distance (3780), then your answer should be correct.

Answer 3

D = d1 + d2
3780 = 4x + 4(x+45)
3780 = 8x + 180
3780 - 180 = 8x
x = 450 mph
V1 = 450mph
V2 = 450+45 = 495 mph
d1 = 4*450 = 1800mile
d2 = 4*495 = 1980mile
4980 = 1800 + 1980 (Checks)

Answer 4

495mph and 450mph