SOLUTION: a man travels 10km in 50mins if he runs for 8km and walks for 2km. if he runs 4km and walks 6km, his time is 1h 15mins. find his running and walking speed.

Question 723994: a man travels 10km in 50mins if he runs for 8km and walks for 2km. if he runs 4km and walks 6km, his time is 1h 15mins. find his running and walking speed.

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
a man travels 10km in 50mins if he runs for 8km and walks for 2km.
if he runs 4km and walks 6km, his time is 1h 15mins.
find his running and walking speed.
:
Change 50 min to 5/6 hr
Change 1 hr 15 min to 5/4 hr
:
Let r = his running speed in km/hr
Let w = his walking speed
:
Write a time equation for each scenario; time = dist/speed
:
+ =
and
+ =
:
Multiply the above by 2 and subtract the 1st equation
+ =
+ =
--------------------------------- subtraction eliminates r, find w
0 + = -
multiply by 12w, resulting in
12(10) = 3w(10) - 2w(5)
120 = 30w - 10w
120 = 20w
w = 120/20
w = 6 km/hr walking
:
Replace w with 6 in the 1st equation
+ =
= -
=
cross multiply
3r = 8 * 6
3r = 489
r = 48/3
r = 16 km/hr running
:
;
Check solution in the 2nd equation
+ =

RELATED QUESTIONS
A man travels 10km in 50mins if he runs for 8km and walks for 2km. If he runs 4km and... (answered by ankor@dixie-net.com)

Buduli covers a distance of 8km to his house in 1hour.He walks part of the distance at... (answered by ikleyn,MathTherapy)

Each day, Amit runs nine miles and then walks one mile. He runs 10 mph faster than he... (answered by mananth)

Arif walks for x hours at 5km/h and runs for y hours at 10km/h. He travels a total of... (answered by Alan3354,jessica43)

An athlete runs for 2 hours and walks for 1 hour to cover a distance of 40km. If he runs... (answered by josgarithmetic)

A man walks due west for 4km.He then changes direction and walks on a bearing of... (answered by Boreal)

Julia runs out of gas. she walks 4km west and then 2km south looking for a gas station.... (answered by ikleyn)

A man misses the train by 2 minutes if he walks to the the station at an average speed of (answered by jorel1380)

Lordina has to cover 4km to catch a bus ,she walks part of the distance at 3kmph and runs (answered by jorel555,Aldorozos)