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Jane leaves her house at 12:30PM and bikes at 12 miles per hour to Marta's house. She stays at Marta's house for 90 minutes. Both girls walk back to Jane's house along the same route at 2.5 miles per hour. They arrive at Jane's house at 3:30PM. How far is Jane's house.

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onyebuchinnaji

The distance of Jane's house is 3.12 miles.

Total time spent by Jane during the journey

The time spent by Jane during the journey is calculated as follows;

from 12:30 PM to 3:30 PM = 3 hours

time  spent by Jane biking  = 3 hours - 90 minutes

                                              = 3 hours - 1.5 hours

                                              = 1.5 hours

Distance between Jane and Marta's house

let the time taken during her first motion before coming back = t

12t = 2.5(1.5 - t)

12t = 3.75 - 2.5t

14.5t = 3.75

t = 3.75/14.5

t = 0.26 hr

distance = 12 miles/hr x 0.26 hr

distance = 3.12 miles

Thus, the distance of Jane's house is 3.12 miles.

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