SOLUTION: It takes a man 23 min. longer to jog 5 mi than it takes his son to run the same distance. However, if the man doubles his rate, he can run the distance in 1 min. less than his son.
Algebra.Com
Question 505896: It takes a man 23 min. longer to jog 5 mi than it takes his son to run the same distance. However, if the man doubles his rate, he can run the distance in 1 min. less than his son. What is the man's rate of jogging and what is the son's rate of running?
Found 2 solutions by stanbon, MathTherapy:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
It takes a man 23 min. longer to jog 5 mi than it takes his son to run the same distance. However, if the man doubles his rate, he can run the distance in 1 min. less than his son. What is the man's rate of jogging and what is the son's rate of running?
----
Father DATA:
distance = 5 mi ; time = t+(23/60) hrs ; rate = d/t = 5/[t+(23/60)] mph
----------------
Son DATA:
distance = 5 mi ; time = t hrs ; rate = d/t = 5/t mph
-----
New Father DATA:
distance = 5 mi; rate = 10/[t+(23/60)] mph ; time = d/r = [t+(23/60)]/2 hrs
----
Equation:
son time - new father time = 1/60 hr
t - [t+(23/60)]/2 = 1/60
2t - t - (23/60) = 1/60
t = 22/60 hr = 22 minutes (son's time)
Son's rate = 5mi/(11/60)hr = 300/11 = 27.27 mph
-----
father time = t+(23/60) = 45 minutes
Father's rate = 5mi/(3/4)hr = 20/3 = 6 2/3 mph
===================================================
Cheers,
Stan H.
==============
Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!
Let man’s rate be miles per hr
Then man’s time to jog 5 miles =
Let son’s rate be miles per hr
Then son’s time to jog 5 miles =
Since man takes 23 min longer than his son to jog 5 miles, then we have: man’s time – son’s time = 23 mins, or:
Since doubling the man’s rate would make him cover the 5 miles in 1 min less than son, then we can say that: son’s time - man’s time = 1 min, or:
-----
We now have:
---- eq (i)
---- eq (ii)
------- Adding eqs (i) & (ii)
----- Reducing right-side of equation
------- Multiplying by LCD,
, or man's speed = , or mph
---- Substituting or for in eq (i)
----- Cross-multiplying
, or son's speed = , or mph
-----------
Check
-----------
Man’s time = son’s time + 23 mins
+ 23 mins
(TRUE)
Doubling speed, man’s time = son’s time – 1 min
- 1 min
(TRUE)
Send comments and “thank-yous” to MathMadEzy@aol.com
RELATED QUESTIONS
A man can ride his bike 18 miles in the same time it takes him to run 6 miles. He can... (answered by TimothyLamb,MathTherapy)
It takes a man 5 hours to wash and wax the family car. If his teenage son helps him, it... (answered by josgarithmetic)
If a man takes 7 days to dig his garden and the son takes 4 days. How long would it take... (answered by tommyt3rd)
Hi
A man walks at 4/5 of his speed to his office and is late by 5 min. What is the time... (answered by ikleyn)
It takes a man 4 hours to wash and wax the family car. If his teenage son helps him, it... (answered by ewatrrr)
A man can mow his lawn in 4 hours. His son can do the job in 3 hours. If the son takes... (answered by VFBundy)
A man can run 3 kilometers faster than he walks. It takes him 4 hours to run 30... (answered by Tatiana_Stebko,ankor@dixie-net.com)
A man can paint a room by himself in 8 hours and it takes his son 12 hours to do the same (answered by Earlsdon)
a man can paint a room by himself in 8 hours it takes his son 12 hours to do the same... (answered by nerdybill)