M and B leave their campsite and walk in opposite directions around a lake. If the shoreline is 15 miles long, M walks 0.5 miles per hour faster than B and they meet in 2 hours...how fast does each walk?

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Answer 1 · 2016-06-23T11:41:04

M walks at 4mph, B walks at 3.5mph

#S_x# denotes speed of person x

#S_M = S_B + 0.5# as M is walking 0.5 mph faster than B

#D= S_M t# t being the amount of times passed (in hours)

#D=15 - (S_Bt)# we know since M is walking faster B must meet at some location minus from the max location (as continues walking round)

#15-(S_Bt) = S_Mt# since D = D

#t = 2# as 2 hours - substitute in

#15-S_B(2) = S_M(2)#

#S_M = S_B+0.5# so (as travelling faster) - substitute in

#15-2S_B = 2(S_B+0.5)# expand and simplify

#S_B = 3.5# Speed of B = 3.5mph

#S_M = S_B + 0.5#
#S_M = 3.5 + 0.5 = 4# Speed of M = 4mph