Taxi A travels 12mph faster than taxi B Taxi A travels 140 m

Taxi A travels 12mph faster than taxi B. Taxi A travels 140 miles in the same time it takes taxi B to travel 108 miles. Find the speed of each taxi.

Solution

Distance(d) equals Rate(r) times Time(t) or d=rt;t=d/r and r=d/t
Let r=rate of taxi B
Then r+12=rate of taxi A
Time it takes taxi A to travel 140 mi=140/(r+12)
Time it takes taxi B to travel 108 mi=108/r
Now we are told that the above two times are equal. So:
140/(r+12)=108/r multiply both sides by r(r+12) to get rid of fractions. (Note: cross-multiplying yields the same result)
140r=108(r+12) get rid of parens (distributive law)
140r=108r+1296 subtract 108r from both sides
140r-108r=108r+1296-108r collect like terms
32r=1296 divide both sides by 32
r=40.5 mph-----------------------------------speed of taxi B
r+12=40.5+12=52.5 mph-------------------------speed of taxi A
CK
140/(52.5)=108/(40.5)
2.666666667=2.666666667