Here is my homework question: Two boats start together and race across a 72 km w

Question

Here is my homework question:
Two boats start together and race across a 72 km wide lake and back. Boat A goes acrossat 72 km/h and returnsat 72 km/h. Boat B goesacross at 36 km/h, and itscrew, realizing how far behind it is getting, returnsat 108 km/h. Turnaroundtimes are negligible, and the boat that completes the round-tripfirst wins. What is the average velocity of the winning boat?
I correctlycalculated that the winning boat was boat A and that it won by 72km. But when I answered that it's average velocity was 72 km/hr(because it traveled 144 km in two hours), it said that I wasincorrect. What am I missing here?


Here is my homework question:

I correctlycalculated that the winning boat was boat A and that it won by 72km. But when I answered that it's average velocity was 72 km/hr(because it traveled 144 km in two hours), it said that I wasincorrect. What am I missing here?

Explanation / Answer

Boat A XA = VA1(1/2)t+ VA2(1/2)t XA = 2(1/2)(72km/hr)t XA = (72km/hr)t but XA = 2(72km) = 144km t = (144km)/(72km/hr) t = 2 hr ---- Boat B (we must split into two position intervals, because ithad two velocities) XB1 = VB1t1 XB1 = (36km/hr)t1 But XB1 = 72km (36km/hr)t1 = 72km t1 = 2 hr So we know right there, that Boat A finishes round trip asBoat B is just halfway (72 km) ------ Winning boat's average velocity = constant velocity =72 km/hr ------- I honestly can't say that you're doing anything wronghere..... beats me. But XB1 = 72km (36km/hr)t1 = 72km t1 = 2 hr So we know right there, that Boat A finishes round trip asBoat B is just halfway (72 km) ------ Winning boat's average velocity = constant velocity =72 km/hr ------- I honestly can't say that you're doing anything wronghere..... beats me.

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