Question 109160

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



Hope this helps---ptaylor