Question 29014: Please help with the following word problem.
"Trains at each end of the 50.0-km long Eurotunnel under the English Channel start at the same time into the tunnel. Find their speeds if the train from France travels 8.0-km/h faster than the train from England and they pass in 17.0 min"
I know I need to use the formula d=rt, but not sure how to write the equation to solve it.
Thank you,
Jackie
Answer by josmiceli(19441)   (Show Source):
You can put this solution on YOUR website! there are two indepenant moving objects, so each one has its own equation
d[1] = r[1] x t[1]
d[2] = r[2] x t[2]
t[1] = t[2] = 17 min
that's because they both start at the same time and meet in 17 min.
you can say d[2] = 50 - d[1]
that's since the distances they travel add up to 50 km
also, r[2] = r[1] + 8 km/hr
since t is in minutes, convert this to km/min
8 km/hr x 1 hr/60 min = 2/15 km/min
[a] d[1] = r[1] x 17
[b] 50 - d[1] = (r[1] + 2/15) x 17
substituting [a] into [b]
50 - r[1] x 17 = r[1] x 17 + 34/15
divide through by 17
50/17 -r[1] = r[1] + 2/15
add r[1] to both sides
2r[1] = 50/17 - 2/15
r[1] = 25/17 - 1/15
r[1] = 1.404
r[2] = r[1] + 2/15 = 1.537
these rates are in km/min
to convert to km/hr multiply by 60 min/hr
check answers
d[1] = r[1] x 17
d[1] = 1.404 x 17
d[1] = 23.87 km
d[2] = (r[1] + 2/15) x 17
d[2] = (1.404 + .133) x 17
d[2] = 26.13 km
23.87 + 26.13 = 50 km
answers check
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