Two cyclists left simultaneously from cities a and b heading towards each other at constant rates and met in 5 hours. the rate of the cyclist from a was 3 mph less than the rate of the other cyclist. if the cyclist from b had started moving 30 minutes later than the other cyclist, then the two cyclists would have met 31.8 miles away from a. what is the distance between a and b, in miles?

75 miles

Step-by-step explanation:

Let x mph be the cyclist A rate, then x+3 mph is the cyclist B rate.

1. In 1 hour they both traveled x+x+3=2x+3 miles. In 5 hours they traveled

2. Cyclist A spent hours to travel 31.8 miles. If the cyclist from B had started moving 30 minutes (1/2 hour) later than the cyclist A, then he spent hours to travel the rest of the distance. In total they both traveled the whole distance 10x+15 miles, thus

Solve this equation. Multiply it by 2x:

The rate cannot be negative, thus, x=6 mph.

Hence, the distance between cities A and B is

triangle and cube

step-by-step explanation: