Question 81850
Knowing the distance is not necessary to solve this problem.
Use the distance formula {{{d = rt}}}for each way.
{{{d = r[1]t[1]}}} and
{{{d = r[2]t[2]}}} Where r is the rate (speed) and t is the time of travel.
You know that the distance, d, is the same in both cases.
You also know that {{{r[2]=r[1]+7}}}
You know that {{{t[1] = 10}}} and{{{t[2] = 9}}}
Making the appropriate substitutions, you'll get:
{{{d = r[1]*10}}}
{{{d = (r[1]+7)*9}}}
Set these two equations equal to each other and solve for {{{r[1]}}}
{{{r[1]*10 = (r[1]+7)*9}}} Simplify.
{{{10r[1] = 9r[1]+63}}} Subtract {{{9r[1]}}} from both sides.
{{{r[1] = 63}}}mph
{{{r[2] = r[1]+7}}}
{{{r[2] = 63+7}}}
{{{r[2] = 70}}}mph
Check:
{{{63*10 = 630}}}miles. This is the distance one-way.
{{{70*9 = 630}}}miles.