Q:

# Bill spends two days driving from point a to pointb. on the first day, he drove 2 hours longer and at an average speed 5 miles per hour faster than he drove on the second day. if during the two days he drove a total of 680 miles over the course of 18 hours, what was his average speed on the second day, in miles per hour?

Accepted Solution

A:
Answer: his average speed on the second day is 35 miles per hourStep-by-step explanation:Bill spends two days driving from point a to point bLet x = his speed on the first day.Let y = his speed on the second daySpeed = distance / timeTime = distance / speedTotal time spent on the trip is 18 hoursLet time that he spent on the first day be t hoursTime that he spent on the second day will be 18 - tBill drove 2 hours longer on the second day than on the first day. This means t = 18 - t + 2t+t = 18+22t = 20t = 10He spent 10 hours on the first day.He spent 18-10 = 8hours on the second day.Bill drove at an average speed of 5 miles per hour faster than he drove on the second day. This means thatx = y + 5 - - - - - - - -- 1Distance travelled on the first day = speed on the first day Γ time spent. This becomes10 Γ x = 10x milesDistance travelled on the second day = speed on the second day Γ time spent. This becomes8 Γ y = 8y milesHe drove a total of 680 miles over the course of the 18 hours. This means that 10x + 8y = 680 - - - - - - - - 2Substituting equation 1 into equation 2, it becomes10(y + 5) + 8y = 68010y + 50 + 8y = 68010y + 8y = 680 - 5018y = 630y = 630/18 = 35 miles per hourx = y + 5 = 35 + 5 x = 40 miles per hour