During the summer Brittanys commute to work is 32 miles She

During the summer, Brittany\'s commute to work is 32 miles. She rides her bike at 9 mph to the metro station. She then takes the metro to work, which travels at 40 mph. If she spends 17 minutes less on the bike than on the metro, what is the distance in miles from her house to the metro? (Round your answer to one decimal place.)

Solution

Total distance = 32 miles.

She rides her bike at 9 mph

She travels by metro at a speed of 40 mph.

She spends 17 minutes less on bike than on metro.

Let the time taken by bike be \"t\"         //    here \"t\" in hrs

distance Therefore time taken by metro = t + 17 = t + 17 / 60         // divide by \"60\" to convert minutes to hour

Distance = Speed * Time

total distance = distance covered by bike + distance covered by metro

distance covered by bike = 9 * t

distance covered by metro = 40 * (t + 17/60)

total distance = distance covered by bike + distance covered by metro

32 = 9t + 40 * (t + 17/60)

32 = 9t + 40t + 34/3

32 = 49t + 34/3

49t = 32 - 34/3

49t = 96/3 - 34/3

49t = 62/3

t = 0.42 hrs

so the distance from metro = distance covered by bike

distance covered by bike = 9*t = > 9 *0.42 = 3.78 miles

distance from metro = 3.8 miles