Victoria jogs 12 miles to the park along a flat trail and then returns by jogging on an 20 mile hilly trail. The uphill time is 2 hours more that the downhill time. Downhill 12 mph 12 miles 12 mph = 1 hour Uphill 12 − 8 = 4 mph 12 miles 4 mph = 3 hours. Is 12 mph a reasonable speed for biking downhill? Yes.ĭownhill 12 mph 12 miles 12 mph = 1 hour Uphill 12 − 8 = 4 mph 12 miles 4 mph = 3 hours. The uphill time is 2 more than the downhill time. He took 2 hours longer uphill than downhill. The distance is the same in both directions. His uphill speed is 8 miles per hour slower. We are looking for Hamilton’s downhill speed. Run 8 mph 8 miles 8 mph = 1 hour Bike 12 mph 24 miles 12 mph = 2 hours Run 8 mph 8 miles 8 mph = 1 hour Bike 12 mph 24 miles 12 mph = 2 hours If Jazmine’s running rate is 4, then her biking rate, Is 8 mph a reasonable running speed? Yes. ( 3 r + 4 ) = 0 ( r − 8 ) = 0 ( 3 r + 4 ) = 0 ( r − 8 ) = 0Ī negative speed does not make sense in this problem, Translate the sentence to get the equation.
Her time plus the time biking is 3 hours. The distances are given, enter them into the chart. Her biking speed is 4 miles faster than her We are looking for Jazmine’s running speed. If the plane is traveling 150 mph and the wind is 30 mph,
Is 150 mph a reasonable speed for an airplane? Yes. We know the times are equal and so we writeĢ00 r − 30 = 300 r + 30 200 r − 30 = 300 r + 30 We divide the distance by the rate in each row, and place the expression in the time column. The wind decreases its speed and the rate is r − 30. The wind increases its speed and so the rate is r + 30. We are looking for the speed of the airplane. We fill in the chart to organize the information.