Word problems involving distance?

Question

I'm really not quite sure how I'm supposed to do these two word problems.

1) A person travels to a destination at a rate of 50mph and returns the next day at a rate of 40mph. If the time returning is one hour more than the time going, how many miles are traveled in all?

2) A person drives to a destination at a rate of 30mph and returns over the same route at 50mph. How far is the destination if the time returning is one hour less than the time going?

Answer 1

1.) D = RT (distance = product of the speed and time) is the important equation here.

R(1) = initial speed = 50 mph. R(2) = return speed = 40 mph.

Since the person is traveling the same distance to and from their destination, then D(1) = D(2). Now all you have to deal with is the time traveled, because you know R(1) and R(2). Let T be the time it took to travel to the destination, and T + 1 be the time required to return. Now set D(1) = D(2) and find T.

D(1) = R(1)T
D(2) = R(2)(T + 1)
R(1)T = R(2)(T + 1)
50T = 40(T + 1)
50T = 40T + 40
10T = 40
T = 4 and T + 1 = 5.
D(1) = 50 mph (4 h) = 200 mi.
D(2) = 40 mph (5 h) = 200 mi.

Now add D(1) and D(2) to find the total distance traveled.

D(1) + D(2) = 200 mi + 200 m = 400 mi.

2.) The same principle is involved here. All you need to do is set both distances equal to each other and then solve for T. When you have found that, just multiply that by the speed to find D. In this instance though the return time is one hour shorter than the time traveling out. So let the return time be T - 1.

D(1) = D(2)
R(1)T = R(2)(T - 1)
30T = 50(T - 1)
30T = 50T - 50
50 = 20T
2.5 = T and T - 1 = 1.5.
D = 30 mph (2.5 h) = 75 mi.

To verify that the figures are correct, compute the distance back as well. They should be equal.

D = 50 mph (1.5 h) = 75 mi.

So our figures seem to be correct.

Answer 2

1.
d = 50t = 40(t+1)
Solve for t,
t = 4 hours
2d = 2(50t) = 2[50(4)] = 400 miles, total distance traveled.

2.
d = 30t = 50(t-1)
Solve for t,
t = 2.5 hours
d = 3t = 3(2.5) = 7.5 miles, one way distance.

Answer 3

1)
d = one way distance
2d = round trip distance

d = 50t = 40(t + 1)
50t = 40t + 40
10t = 40
t = 4

d = 50(4) = 200
2d = 2*200 = 400 miles
______________________

(2)
d = distance to destination

d = 50t = 30(t + 1)
50t = 30t + 30
20t = 30
t = 3/2

d = 50(3/2) = 75 miles

Answer 4

1= 200 mi.