Question

Traveling from San Antonio to Dallas, you fist pass through Austin and then Waco before reading Dallas, a total distance of 280 miles. From Austin to Waco is 30 miles faster than from San Antonio to Austin, and also 20 miles farther than from Waco to Dallas. How far is it from Waco to Dallas?

Answer 1

The answer is 70 miles.

If we express distances as following:
T - total distance
a - distance from San Antonio to Austin
b - distance from Austin to Waco
c - distance from Waco to Dallas
Then:
T = 280 mi
b = a - 30 mi        ⇒ a = b + 30
b = c + 20 mi       ⇒ c = b - 20

T = a + b + c
⇒ a + b + c = 280
⇒ b + 30 + b + b - 20 = 280
⇒ 3b +10 = 280
⇒ 3b = 280 - 10
⇒ 3b = 270
⇒ b = 90 mi.

Distance from Waco to Dallas is c.
c = b - 20
⇒ c = 90 - 20
⇒ c = 70 mi

Therefore, distance from Waco to Dallas is 70 miles.