Question

four cities lie along a straight highway in this order city a, city, city c, city d. The distance from city a to city b is 5 times the distance from city b to city c. The distance from city a to city d is 2 times the distance from city a to city d. the distance between city d and city c is 10 miles. What are the distances between the cities?

Answer 1

The distance from city A to city B is 50 miles, the distance from city B to city C is 10 miles, and the distance from city A to city D is 100 miles.

Step-by-step explanation:

Let's assign the distance from city A to city B as x. Since the distance from city A to city B is 5 times the distance from city B to city C, we can write this as x = 5y, where y is the distance from city B to city C.

The distance from city A to city D is 2 times the distance from city A to city B, so we have 2x = 2(5y) = 10y.

We know that the distance between city D and city C is 10 miles, so y = 10. Substituting this value into the equations, we can find the distances:

Distance from city A to city B: x = 5y = 5(10) = 50 miles

Distance from city B to city C: y = 10 miles

Distance from city A to city D: 2x = 2(50) = 100 miles