Question 158868: The speed of train A is 16 mph slower than the speed of train B. Train A travels 220 miles in the same time it takes train B to travel 300 miles. Find the speed of each train.
Answer by gonzo(654)   (Show Source):
You can put this solution on YOUR website! rate * time = distance
train A travels 16 mph slower than train B. if rate of train A is x miles per hour, then rate of train B is (x+16) miles per hour.
let T = time in hours,
if A travels 220 miles in T hours, then x*T = 220.
if B travels 300 miles in T hours, then (x+16)*T = 300.
solving for T, we get
T = 220/x from the first equation, and
T = 300/(x+16) from the second equation.
since both equations equal T, they must be equal to each other, so
220/x = 300/(x+16)
solving for x, we multiply both sides of the equation by x*(x+16) to remove the denominators. equation becomes
220*(x+16) = 300*x
this becomes
220*x + 220*16 = 300*x
subtracting 220*x from both sides of the equations gets
220*16 = 300*x - 220*x
this becomes
3520 = 80*x
which becomes
x = 44 mph
it looks like train A is traveling 44 mph and train B is traveling 60 mph.
once we know this we can solve for T.
for train A, T = 220/44 = 5 hours
for train B, T = 300/60 = 5 hours
60 mph minus 44 mph = 16 mph so train B is traveling 16 mph faster than train A.
answer checks out, so answer is:
train A is traveling at 44 mph.
train B is traveling at 16 mph.
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