Bob and wendy left home to walk together to a restaurant for dinner. they started out walking at a constant pace of 3 mph. at precisely the halfway point, bob realized he had forgotten to lock the front door of their home. wendy continued on to the restaurant at the same constant pace. meanwhile, bob, traveling at a new constant speed on the same route, returned home to lock the door and then went to the restaurant to join wendy. how long?

(ab + 9b)/6b hour

Explanation:

Assuming the distance from their home to the restaurant is a meter

Average speed = 3mph

At halfway point, they had walked a/2 meter

Time taken to reach halfway point = a/2 ÷ 3 = a/6 hour

Assuming Bob's new constant speed is bmph

Time taken to return home from halfway point = a/2 ÷ b = a/2b hour

Time taken to get to the restaurant from home = a/b hour

Total taken = a/6 + a/2b + a/b = (ab + 9b)/6b hour

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