two trains, train a and train b, simultaneously depart station a and station b. station a and station b are 252.5 miles apart from each other. train a is moving at 124.7mph towards station b, and train b is moving at 253.5mph towards station a. if both trains departed at 10:00am and it is now 10:08, how much longer until both trains pass each other? [a] 31.054 minutes [b] 16.232 minutes [c] 32.049 minutes [d] 32.058 minutes

Question

04-09-2016
Mathematics

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two trains, train a and train b, simultaneously depart station a and station b. station a and station b are 252.5 miles apart from each other. train a is moving at 124.7mph towards station b, and train b is moving at 253.5mph towards station a. if both trains departed at 10:00am and it is now 10:08, how much longer until both trains pass each other? [a] 31.054 minutes [b] 16.232 minutes [c] 32.049 minutes [d] 32.058 minutes

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ok

first find how far they have traveled so we will know how much more they need to cover

remmeber distance=speed times time

after 8 mins (from 10 to 10:08) or 8/60 or 4/30 or 2/15 or 1/7 hours

train a traveled 124.7 times 1/7=124.7/7 miles aprox 16.62666666666 miles

train b traveld 253.5 times 1/7=253.5/7 miles aprox 36.2142857143 miles

so subtract that from total distance
252.5-16.626666666-36.2142857143= about 202 miles
use fractions
3031.1/15 miles apart
how long till they pass

means that how long will they together make up that distance
it is 't' time
distance=speed time time

total distance=d1+d2
d1=124.7 times t
d2=235.5 times t
total distance=3031.1/15
3031.1/15=124.7t+253.5t
3031.1/15=378.2t
times both sides by 15
3031.1=5673t
divide both sides by 5673
0.534302838=t
about 32.05817028 mins

answer is D