On Monday, Crystal drives from San Antonio to Dallas at a constant speed.
On her return trip on Tuesday, she initially drives 10% faster than her Monday
speed. However, during the last part of her trip, she runs into traffic and has to
drive 30% slower than her Monday speed. As a result, her Tuesday trip takes
exactly as long as her Monday trip. What fraction of the distance of her
Tuesday trip does she travel at the faster speed? Express your answer
as a common fraction.
Let her constant speed on Monday = S
Let the distance from San Antonio to Dallas =1000 miles
[Note: The distance does not matter, since the portion of the distance where she traveled at 10% faster will be constant]
Let the portion of the distance where she drove 10% faster =D
The portion of the distance where she drove at 30% slower =1000 - D
1000/S =D/(1.1S) + (1000-D)/(0.7S), solve for D
D =825 miles
825 / 1000 =82.5% portion of the distance where she drove at the faster speed.