# 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?

Jun 23, 2016

M walks at 4mph, B walks at 3.5mph

#### Explanation:

${S}_{x}$ 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)

$D = 15 - \left({S}_{B} t\right)$ we know since M is walking faster B must meet at some location minus from the max location (as continues walking round)

$15 - \left({S}_{B} t\right) = {S}_{M} t$ since D = D

$t = 2$ as 2 hours - substitute in

$15 - {S}_{B} \left(2\right) = {S}_{M} \left(2\right)$

${S}_{M} = {S}_{B} + 0.5$ so (as travelling faster) - substitute in

$15 - 2 {S}_{B} = 2 \left({S}_{B} + 0.5\right)$ 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