SOLUTION: To travel 154 miles, it takes Sue, riding a moped, 3 hours less time than it takes Doreen to travel 70 miles riding a bicycle. Sue travels 15 miles per hour faster than Doreen. Fin
Algebra.Com
Question 761492: To travel 154 miles, it takes Sue, riding a moped, 3 hours less time than it takes Doreen to travel 70 miles riding a bicycle. Sue travels 15 miles per hour faster than Doreen. Find the times and rates of both girls.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
To travel 154 miles, it takes Sue, riding a moped, 3 hours less time than it takes Doreen to travel 70 miles riding a bicycle. Sue travels 15 miles per hour faster than Doreen. Find the times and rates of both girls.
---------------
Sue DATA:
distance = 154 miles ; time = x-3 hrs ; rate = d/t = 154/(x-3) mph
------------------
Doreen DATA:
distance = 70 miles ; time = x hrs ; rate = 70/x mph
------------------
Equation:
rate - rate = 15 mph
154/(x-3) - 70/x = 15
154x - 70(x-3)=15x(x-3)
----------------------------
154x - 70x + 210 = 15x^2 - 15x
84x + 210 = 15x^2 - 15x
-----
15x^2 - 99x - 210 = 0
5x^2 - 33x - 70 = 0
----------------
Positive solution:
x = 8.89 hrs (Doreen time) ; 70/8.289 = 8.445 mph (Doreen rate)
----
x-3 = 5.89 hrs (Sue time) ; 154/5.89 = 18.24 mph (Sue rate)
===================
Cheers,
Stan H.
===================
RELATED QUESTIONS
To travel 154 miles, it takes Sue, riding a moped, 2 hours less time than it takes Doreen (answered by josgarithmetic,MathTherapy)
To travel 84 miles, it takes Sue, riding a moped, 3 hours less time than it takes Doreen... (answered by josmiceli)
To travel 110 miles, it takes Sue, riding a moped, 3 hours less time than it takes Doreen (answered by stanbon)
To travel 88 miles, it takes Sue, riding a moped, 4 hours less time than it takes Doreen... (answered by stanbon,mananth)
To travel 60 miles, it takes Sue, riding a moped, 2 hours less time than it takes Doreen... (answered by ewatrrr)
To travel 125 miles, it takes Sue, riding a moped, 2 hours less time than it takes Doreen (answered by solver91311)
To travel 60 miles, it takes Sue, riding a moped, 2 hours8
less time than it takes... (answered by josmiceli)
a car can travel 75 miles in the same amount of time that it takes a moped to travel 25... (answered by josmiceli)
Jenny, who rides a moped, takes 2 hours less to travel 60 miles than Maureen takes to... (answered by stanbon)