Nathan is out rafting. He rafts 16 miles with the river current. At the end of 16 miles, he turns around and rafts the same distance against the river current. The journey takes him 4 hours overall. If he can raft at a speed of 9 mph in still water, what is the speed of the current of the river he is in?A 5 mphB 4 mphC 6 mphD 3 mph
Accepted Solution
A:
Answer:Speed of the current of the river = 3 mphStep-by-step explanation:Let the speed of the current of the river he is in be u mph.He rafts 16 miles with the river current. At the end of 16 miles, he turns around and rafts the same distance against the river current. The journey takes him 4 hours overall.He can raft at a speed of 9 mph in still waterThat is [tex]\frac{16}{9+u}+\frac{16}{9-u}=4\\\\\frac{4}{9+u}+\frac{4}{9-u}=1\\\\36+4u+36-4u=81-u^2\\\\u^2=81-72=9\\\\u=3mph[/tex]Speed of the current of the river = 3 mph