A rideshare app charges $2 per trip plus $0.4 per mile. A competitor charges $1 for the first 6 miles plus $0.5 per mile for every additional mile. For what length trip would the two services charge the same amount?

A. 10 miles
B. 18 miles
C. 20 miles
D. 40 miles

Can you craft an algebraic equation to solve this directly – or is plugging in the answers the way to go?

 

Starting from the answer choices works nicely here, and you know I love doing that, but since you asked, of course an equation is also viable. Say x is the number of miles in the trip. The first app charges 2+0.4x, and the second app (this is the tricky one) charges 1+0.5(x-6). That’s only for a trip greater than 6 miles, really, but all the answer choices are greater than 6, so we’re good here. Now just set them equal and solve!

2+0.4x=1+0.5(x-6)
2+0.4x=1+0.5x-3
2+0.4x=-2+0.5x
4=0.1x
40=x