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If the jogger can run at an average speed of 5.3 miles per hour up the slope and

ID: 3168980 • Letter: I

Question

If the jogger can run at an average speed of 5.3 miles per hour up the slope and 6.7 miles per hours down the slope, how long, in hours will it take for the jogger to cover 2 miles by going up hill for 1 mile and then returning 1 mile back down the hil? [Give an exact answer expressed as a fraction in simplest terms and then give a decimal approximation correct to three decimal places] 8. Write an algebraic expression for the total time, in hours, that it takes the jogger to cover 2 miles by going up the hill for 1 mile and then returning 1 mile back down the hill f the jogger runs uphill at an average speed that is c miles per hour slower than the level-ground speed df 6 miles per hour and runs downhill at an average speed that is c miles per hour faster than the level group speed of 6 miles per hour. Simplify your answer to a single algebraic fraction. Verify that your expression gives the correct answers for Questions 6 and 7 above. Original Task developed by Georgia Department of Education 2008 © Math 1-Unit 2 Modified by M. Winking il. wiseone@mindspring.com p.1

Explanation / Answer

Total distance to be covered = 2 miles; Of which 1 mile is uphill and 1 mil is downhill;

Speed up hill = 5.3 miles per hour; Distance to be covered uphill = 1 mile; So, time taken will be = distance/ speed
tu = 1/5.3 = 1/5.3 hours

Speed downhill = 6.7 miles/hour; Distance to be covered downhill=1 mile; So, time taken will be = distance/ speed
td = 1/6.7 = 1/6.7 hours
Total time to be takn = t = tu + td = 1/5.3 + 1/6.7 = 6.7+5.3 / (6.7)(5.3) = 12/(6.7*5.3) = 12/35.51 = 1200/3551 hours

Thus, total time taken in hours = 1200/3551 hours
In decimal form total time taken = 0.3379 ~= 0.338 hours
Thus, total time taken in 3 decimal places = 0.338 hours