question listed below

Question

Jon recently drove to visit his parents who live600  miles away. On his way there his average speed was 14 miles per hour faster than on his way home (he ran into some bad weather). If Jon spent a total of 25 hours driving, find the two rates.

Answer 1

Let x = his time driving back and let 25-x = time driving the first 300 miles. Average speed is distance divided by time driving. Speed going was 300/(25-x). Speed driving back was 300/x. 300/(25-x) =300/x + 14 mph.

Solve that last equation for x. Simplified, it should be a quadratic equation that can't be easily factored, so use the quadratic formula. Then substitute x into the formulas for speed each way. An approximation is x=16 hours Then the speed going was about 300/9 or 33 mph. Speed coming back was about 300/16 or approximately 19 mph. 33=19+14. This is just an estimate, but the actual answer rounded off is closest to these integers, 33 mph and 19 mph.On an SAT multiple choice question, just pick the answer closest to 33 and 19, or use your calculator and do all the calculations to get a closer more exact answer. Or another approach could be to pick some simple numbers for x, such as 10. Substitute 300/10=30 and 300/15=20 30=20+10. We need a little more than 10, as the difference is 14. So we want an x a little less than 10. The smaller the x, the larger the difference in speeds.