Question

You commute to work a distance of 40 miles and return on the same route at the end of the day. Your average rate on the return trip is 30 miles per hour faster than your average rate on the outgoing trip. If the round trip takes 2 hours, use a rational equation and factoring to find your average rate on the outgoing trip to work?

Answer 1

Step-by-step explanation:

Given You commute to work a distance of 40 miles and return on the same route at the end of the day. Your average rate on the return trip is 30 miles per hour faster than your average rate on the outgoing trip. If the round trip takes 2 hours, use a rational equation and factoring to find your average rate on the outgoing trip to work?

• Distance = rate x time
• 40 = r x t or t = 40/r
• 40 = (r + 30)(2 – t)
• 40 = (r + 30) (2 – 40 / r)
• 40r = (r + 30)(2r – 40)
• 40r = 2r^2 + 60r – 40r – 1200
• 2r^2 – 20r – 1200 = 0
• 2r^2 – 60r + 40r – 1200 = 0
• 2r(r – 30) + 40(r – 30) = 0
• (r – 30)(2r + 40) = 0
• So r = 30, r = - 20
• So r = 30 mph for going and  r + 30 = 30 + 30 = 60 mph
• Also time will be t = 40 / r = 40 / 30 = 4/3 hours
•                         And t = 40 / 60 = 2/3 hours for outgoing
• Reference link will be

https://brainly.in/question/5265846