Erica's average rate going uphill was 80% of her average rate going downhill over the same route, and it took Erica 10 minutes longer to go up the hill than to go down the hill. What was the total number of minutes Erica spent going uphill and downhill?

Answer 1

distance = rate * time

so, since the distance covered is the same both ways,

.8r * (t+10) = rt
.8rt + 8r = rt
8r = .2rt
8 = .2t
t = 40

so, total time = 40+10 + 40 = 90 minutes