Question

Jack and Rock agree to meet in London for the weekend. Jack travels 164 miles and Rock travels 106 miles. If Jacks rate of speed is 8 mph faster than Rock’s then at what rate of speed does Jack travel?

Answer 1

`v=(s)/(t)\\\\v-velocity;\ s-distance;\ t-time\\\\v=(s)/(t)\to vt=s\to t=(s)/(v)\\---------------------\\v-Rock's\ veloocity\ (mph)\\v+8-Jack's\ velocity\ (mph)\\s_J=164\ mi-Jack's\ distance\\s_R=106\ mi-Rock's\ distance\\t_J=t_R-times\ are\ equal\\\\therefore:(s_R)/(v)=(s_J)/(v+8)\\\\subtitute\ values\ of\ distance:`


`(106)/(v)=(164)/(v+8)\ \ \ \ |cross\ multiply\\\\106(v+8)=164v\\\\106v+848=164v\ \ \ \ |subtract\ 106v\ from\ both\ sides\\\\848=58v\to 58v=848\ \ \ |divide\ btoh\ sides\ by\ 58\\\\v\approx14.6\ (mph)\\\\Answer:\boxed{v+8=(14.6+8)mph=22.6\ mph}`