A boy walks at 5 kilometers per hour for 20 minutes, then at k kilometers per hour for the next 30 minutes, and finally at 4 kilometers per hour for the remaining 10 minutes. If his average speed was approximately 5.83 kilometers per hour for the entire hour, what is the closest value of k?

avg speed = (total distance/total time)

total time = 20 + 30 + 10 = 1 hr

total distance = (3*20)/60 + k + (4*10)/60 = 5/3 + k + 2/3

avg speed = 5.83 = (5/3 + k + 2/3)/1

so, k = (5.83 - 5/3 - 2/3) = 3.49 or 3.5ish

Edit: sth fishy with the solution but I’ll keep it up so that someone else doesn’t make the same mistake

Edit 2: in the total distance equation it should be k/2 instead of k

You need to use Latex since the formatting gets messed up with the * symbol. Also no, 3.5 cannot make sense.

Thanks I’ll keep that in mind!

avg speed=total distance/time

total time =1 hour

total distance=5/3+1/2k+2/3

5.83=5/3+1/2k+2/3

k= 6.99

I think you just missed that k should be k/2 since it’s 30 minutes.

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Thanks for pointing it out!