Question

Judith can ride her bike 2 mi/h faster than kelly. Judith takes 48 min less to travel 50 miles than Kelly does. What is each person's speed in miles per hour??

Answer 1

Let j be judiths speed and k be kellys speed
j = k+2
we also know distance = rate*time
convert 48 min to hours (48/60 = 4/5)
judith:
50 = (t-4/5)*j
kelly:
50 = t*k
set both equations equal to each other and replace j with (k+2)
tk = (t-4/5)(k+2)
tk = tk +2t -4/5k -8/5
0=2t -4/5k -8/5
t = 2/5k + 4/5
substitute this value in for t to find k
50 = k(2/5k +4/5)
2/5k^2 +4/5k -50 = 0
get rid of fractions by multiplying equation by 5
2k^2 +4k -250 =0
quadratic equation gives
k = 10.225 mph
j = k +2
j = 12.225 mph