Question

Question: Greg and Anna drive uphill from Lakeshore to Valley View Point, and back downhill to Lakeshore. They notice that the drive uphill takes 10 minutes less than twice the time to drive downhill. The difference between the time taken to drive uphill and the time to drive downhill is 65 minutes. Write a pair of linear equations to represent the information given above. Be sure to state what the variables represent. Explain how you can change this pair of equations to one linear equation in one variable. Apply your method to find how long the drive uphill takes. Show your work.

Answer 1

For this case, the first thing we must do is define variables:
t1: time to drive uphill
t2: time to drive downhill
We now write the system of equations:
t1 = 2 * t2 - 10
t1 - t2 = 65
To rewrite this problem as an equation with a variable, we clear t2 from equation 2:
t2 = t1 - 65
We substitute equation 1 and obtain an equation with a variable:
t1 = 2 * (t1 - 65) - 10
Clearing t1 we have:
t1 = 2t1 - 130 - 10
t1 = 2t1 - 140
2t1 - t1 = 140
t1 = 140 minutes
Answer:
System of equations:
t1 = 2 * t2 - 10
t1 - t2 = 65
Equation with a variable:
t1 = 2 * (t1 - 65) - 10
the drive uphill takes:
t1 = 140 minutes