Question 1189020
1. The difference in speeds of the two trains is 20mph; the difference in distances over the same amount of time is 80 miles.  So the time traveled is 80/20 = 4 hours.<br>
Train A travels 300 miles in 4 hours, a speed of 75mph; train B travels 220 miles in 4 hours, a speed of 55mph.<br>
ANSWERS: 75 and 55mph<br>
2. Here is an informal method for solving "mixture" problems like this that is nearly always faster and easier than the standard formal algebraic method shown by the other tutor.<br>
(a) All $13,000 invested at 11% would yield $1430 interest; all invested at 12% would yield $1560 interest.
(b) View the three interest amounts $1430, $1490, and $1560 on a number line and observe/calculate that $1490 is $60/$130 = 6/13 of the way from $1430 to $1560.
(c) That means 6/13 of the total was invested at the higher rate.<br>
6/13 of $13,000 is $6000, so<br>
ANSWERS: $6000 invested at 12%, the other $7000 at 11%<br>
CHECK: .12(6000)+.11(7000) =720+770=1490<br>