Question: Greg and Anna drive uphill from Lakeshore to Valley View Point, and back downhill to Lakeshore. They notice that the d
rive 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.
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
Well since we're dealing with the co-efficient of x, then we just have to talk about 18x^3 and divide it by 6x^2 and we get 3x. so the co-eff. is 3 so (A)