Victor and Sharon's Road Trip?

Question

Victor's van travels at a rate of 8mi every 10mins. Sharon's sedan travels at a rate of 20mi every 25mins. If both cars start at the same time, will Sharon's sedan reach point A, 8mi. away, before, at the same time, or after Victor's van? Explain your reasoning. If both cars start at the same time, will Sharon's sedan reach point B (at a distance further down the road) before, at the same time, or after Victor's van? Explain your reasoning.

Answer 1

Both vehicles are traveling at the same speed. Let me explain. If Victor's van is traveling at the rate of 8 miles/10 min, then to find out how many miles he travels in 25 minutes, we multiply the distance traveled during that time by 2.5, because we have multiplied the time by the same factor. We can analyze it as an equivalence ratio:

8/10 = x/25 Now we cross-multiply and solve for x.
10x = 200
x = 20

or, from the relationship found above, we can simply multiply 8/10 by 25 directly to find x.

(8/10)25 = x ----> 8(25/10) = x ----> 8(2.5) = x ----> 20 = x

Hence, Victor is traveling 8 x 2.5 = 20 miles every 25 minutes. This is also Sharon's speed. Therefore, if both leave at the same time and continue at the same constant speed, they will reach the same point at the same time, regardless of how far away that point may be.