Ana rides 5 miles per hour faster than Ben on the same route. Ben takes 3 hours and Ana takes 2 hours. How fast does Ben ride?

1. Let b stand for Ben's speed in miles per hour. 2. Ana rides 5 miles per hour faster, so her speed is b plus 5. 3. Distance equals rate times time, so Ben covers 3b miles. 4. Ana covers 2 times b plus 5 miles. 5. The route is the same for both, so 3b equals 2 times b plus 5. 6. Expanding gives 3b equal to 2b plus 10, so b is 10 miles per hour. 7. Checking, Ben covers 30 miles in 3 hours and Ana covers 30 miles in 2 hours at 15 mph. 8. Answering 15 mph gives Ana's speed rather than Ben's. 9. Answering 5 mph reports the difference between the two speeds. 10. Answering 25 mph adds the two times together, which no equation here supports. _Source: OpenStax Intermediate Algebra (CC BY 4.0), Ch 2 "Solving Linear Equations", section 2.4 Solve Mixture and Uniform Motion Applications_