Question

Four of your friends are planning a morning of boating on the Big Blue River. Two of them plan to start at the Rocky Ford Campground at 9:00 AM and drift down the river with the current in kayaks. The other two plan to start at the parking lot near the US-24 bridge, at the same time as the first pair, and travel upstream in a square-stern canoe with an outboard motor. You own a pickup truck with a high wheelbase, and you are friendly with all the farmers and property owners in the area, so they ask you to pick up them and their boats at the time and place where they will meet. You agree.

You research this section of the Big Blue River and find the following conditions that morning:

Depth: 12.8 feet

Average width: 200 feet

Flow: 13800 ft3/s

Water speed: 8.1 ft/s = 5.5 miles/hr

Water temperature: 78.5 degF

You check a map and find that distance between Rocky Ford Campground and the US-24 bridge parking lot is 4 miles “as the crow flies,” or 8 miles along the river. Your friends with the square-stern canoe say it can travel 2 miles on a still lake in 15 minutes.

(1) At what time should you pick up your friends?

(2) Where should you pick up your friends? (Express this answer in terms of distance downstream from Rocky Ford or upstream from US-24.)

Answer 1

The problem is a combination of river drift finding and use of relative speeds and when dealing with relative speeds it is always adviced to keep one object at rest and give the speed of that object relative to other ,in our case we kept pair A at rest and moved pair B