Esther drove to work in the morning at an average speed of 45 miles per hour. She returned home driving that same route in the evening and averaged 30 miles per hour. If Esther spent a total of one hour commuting to and from work, how many miles did Esther drive to work in the morning?
2007-12-02 14:17:23 · 3 answers · asked by theshortaznswimmer 2 in Science & Mathematics ➔ Mathematics
I believe that her work is more than 1 mile away fyi.
2007-12-02 14:41:46 · update #1
t = d/45 (time in hours = distance in miles/ 45mph)
1-t = d/30 (time coming home)
t + (1-t) = d/45 + d/30
1 = d/45 + d/30
multiply each term by 90
90 = 2d + 3d
90 = 5d
18 = d
(18 miles each way)
check:
in the morning it took her 18/45 hours = 2/5
in the afternoon it took her 18/30 hours = 3/5
2/5 + 3/5 = 1 hour
checks
2007-12-02 14:24:07 · answer #1 · answered by Steve A 7 · 0⤊ 0⤋
Taking the harmonic mean of 30 and 45:
2*30*45/75 = 270/75 = 54/25 mi/hr
Therefore, in 1hr, she went 54/25 mi
Finally, (dividing by 2), her work is 17/25 mi away.
2007-12-02 14:23:54 · answer #2 · answered by wigglyworm91 3 · 0⤊ 2⤋
d = distance in miles
morning commute t₁ = d miles*(1hr/45mi)
evening commute t₂ = d miles* (1hr/30mi)
t₁+ t₂ = 1
d/45 + d/30 = 1
d/45 + 1.5d/45 = 1
d+1.5d = 45
d = 18mi
2007-12-02 14:24:05 · answer #3 · answered by DWRead 7 · 0⤊ 2⤋