How can the geologist estimate how long ago the glacier was in the lower part of the valley?

Divide the distance the glacier has melted back by the current rate at which it is melting back.

Explanation:

dividing the distance the glacier has melted back by the current rate at which it is melting back, the geologist can figure out how long ago the glacier was in the lower part of the valley. For example, if the glacier melted back 2.5 km (2,500 m) and is currently melting back about 15 m per year, the time can be calculated as follows...

Time required for glacier to melt back = 2,500 m ÷ 15 m per year

Time required for glacier to melt back = about 167 years

Most glaciers today are melting back faster than they have in the past. So, the total time is probably longer. Geologists must use additional tools to improve their estimates.