Eudora spent 0.5 hours from home to library and 1.5 hrs from library to home.
Given,
Home to library, Average speed S₁ = 12 km/hr
Average speed S₂ = 76 km/hr
Total distance = 120 km
Total Time = 2 hrs
Let us take the time taken to go from home to library is x. So, from library to school will be 2-x.
S₁ = 12 km/hr
T₁ = x
S₂ = 76 km/hr
T₂ = 2-x
We know that, distance = speed * time
D₁ = 12x
D₂ = 76(2-x) = 152 - 76x
D₁ + D₂ = 120
12x + 152 - 76x = 120
152 - 64x = 120
64x = 32
x = 0.5 hrs
T₂ = 2-x = 2- 0.5 = 1.5 hrs
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