Questions on Geometry: Length, distance, coordinates, metric length answered by real tutors!

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Question 166796: A motorist driving 90 km/h can go from Midland to Shiloh in two hours less than a train that averages 75 km/h. How far apart are the two towns?: A motorist driving 90 km/h can go from Midland to Shiloh in two hours less than a train that averages 75 km/h. How far apart are the two towns?
Answer by Earlsdon(3816) About Me  (Show Source):
You can put this solution on YOUR website!
You can use: d = rt for this problem, where:
d = distance traveled.
r = rate (speed) of travel.
t = time taken to travel distance d at a speed of r.
For the car, r = 90 km/h.
For the train, r = 75 km/h
d[c] = 90(t-2) (t-2 because the car takes 2 hours less than the train).
d[t] = 75t The distance is the same for each, so...
d[c] = d[t]
90(t-2) = 75t
90t-180 = 75t Subtract 75t from both sides.
15t-180 = 0 Add 180 to both sides.
15t = 180 Divide both sides by 15.
t = 12 Now substitute this into either one of the two distance equations.
For the car:
d[c] = 90(t-2) Substitute t = 12.
d[c] = 90(12-2)
d[c] = 90(10)
d[c] = 900km.
For the train:
d[t] = 75t Substitute t = 12.
d[t] = 75(12)
d[t] = 900km.
The towns are 900 km. apart.