SOLUTION: At 7:00 AM, a train leaves a station, traveling at 55 mph. At 7:30 AM, an express train leaves the same station, traveling the same route at 70 mph. How long will it take the expre
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Question 986178: At 7:00 AM, a train leaves a station, traveling at 55 mph. At 7:30 AM, an express train leaves the same station, traveling the same route at 70 mph. How long will it take the express train to overtake the other train, and how far will they be from the station when it does? Found 2 solutions by algebrahouse.com, josgarithmetic:Answer by algebrahouse.com(1659) (Show Source):
First train
d = rt
r = 55
t = time
d = 55t {the equation for the first train}
Second train
d = rt
r = 70
t - 0.5 = time {left 1/2 hour later}
d = 70(t - 0.5) {equation for second train}
When the second train overtakes the first train, their distances will be equal.
55t = 70(t - 0.5) {set distances equal to each other}
55t = 70t - 35 {used distributive property}
-15t = -35 {subtracted 70t from each side}
t = 2.3333 {divided each side by -15}
t = 2 1/3 hours
1/3 of an hour is 20 minutes
t = 2 hours and 20 minutes
Add 2 hours and 20 minutes onto first train's departure time:
7:00 + 2:20
= 9:20
The second train will overtake the first train at 9:20 A.M.
How far will the first train be from the station:
55 mph for 2 hrs. and 20 minutes
= 55 x 2 1/3 {multiplied 55 by 2 1/3 hours}
= 55 x 7/3 {changed 2 1/3 to an improper fraction}
= 385/3 {multiplied through numerators}
= 128 1/3 miles from station
Train speed time distance
EARLY r t+h d
LATER R t d
KNOWN VARIABLES:
r,R,h.
.
h is the delay which occurs in hours before the later train starts from the departure location.
UNKNOWN VARIABLES:
t,d.
t is the time during which the later train travels and overtakes the early train.
Goal is to solve for t and d.
The equality of formulas for d gives
-
Use formula for t to find d.
The problem is now fully solved in symbolic form. Substitute the given values and evaluate t and d.
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