# Math

A boat on a river traveled from City A to City C with a stop at City B. On the first part of the​ trip, the boat traveled at an average speed of 10 miles per hour. From City B to City C the average speed was 15 miles per hour. The entire trip covered 100 miles. How long did the entire trip take if the two parts each took the same number of​ hours?
I don't understand how to solve this question.

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1. let the distance from A to B be x miles
let the distance from B to C be 100-x

I used to have my students create a chart for these, made up of 3 columns
distance, rate and time for the columns, remember: dist = rate x time
so when 2 entries are in, the 3rd can be found

On the side we would state the cases, here the two cases are:
------------------ Dist ......rate......time
from A to B |... x ......|..10 ...|... x/10
from B to A |..100-x .|..15 ...|.. (100-x)/15 , hope this lines up somehow

but the two times are equal

x/10 = (100-x)/15
cross-multiply
15x = 1000 - 10x
25x = 1000
x = 40

Finish it up, filling in the missing parts in the chart

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Reiny
2. 8 hours?

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3. Would have preferred that 8 hours answer without the question mark behind it.

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Reiny

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