Question 1175277
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You have received two response showing similar formal algebraic solutions.<br>
Here is a very different path to the answer that I personally find much faster and easier (if a formal algebraic solution is not required).<br>
This is essentially a mixture problem -- you are mixing some number of hours at 14mph with some number of hours at 7mph and ending up with a total of 119 miles in 11 hours.<br>
You can solve any two-part mixture problem like that in the following way.<br>
All 11 hours at 7mph would cover 77 miles
All 11 hours at 14mph would cover 154 miles
The actual distance covered was 119 miles<br>
Look at the three mileage totals on a number line; with simple calculations, determine that 119 is 42/77 = 6/11 of the way from 77 to 154.
That means 6/11 of the total time was at the higher rate.
6/11 of 11 hours is 6 hours.<br>
ANSWER: 6 hours at 14mph/ 5 hours at 7mph<br>
CHECK: 6(14)+5(7) = 84+35 = 119<br>