finding speeds~~

[owenthakkar]

on a Saturday morning Sue felt like getting some exercise. So she left home at 7 am and walked to a shop along a flat road. When she reached the shop, she immediatley started to walk to an oval along a raod which was never flat. After she came to the oval, she did not stop but turned around and walked along the same route back home. She got home at noon. What was the distance she covered during the morning, if her speeds on the flat road, uphill and down hill were 4km/h, 3km/h and 6km/h respectively?

any help would be nice!! thank you!!
~~ i just cant get my head around the concept of speeds!! :x argh

 

[soroban]

Hello, owenthakkar!

We (two of us) answered this post at another site.
For the benefit of others, here we go . . .

On a Saturday morning Sue felt like getting some exercise.
So she left home at 7 am and walked to a shop along a flat road.
When she reached the shop, she immediatley started to walk to an oval along a road which was never flat.
After she came to the oval, she did not stop but turned around and walked along the same route back home.
She got home at noon.
What was the distance she covered during the morning,
if her speeds on the flat road, uphill and down hill were 4km/h, 3km/h and 6km/h respectively?

Sue walked \(\displaystyle \L x\) km on the flat road at 4 kph. \(\displaystyle \;\)This took \(\displaystyle \L\frac{x}{4}\) hours.

She walked \(\displaystyle \L y\) km on the uneven road at 3 kph. \(\displaystyle \;\)This took \(\displaystyle \L\frac{y}{3}\) hours.

She walked back \(\displaystyle \L y\) km on the uneven road at 6 kph. \(\displaystyle \;\)This took \(\displaystyle \L\frac{y}{6}\) hours.

She walked home \(\displaystyle \L x\) km at 4 kph. \(\displaystyle \;\)This took \(\displaystyle \L\frac{x}{4}\) hours.

Hence, her total walking time is: \(\displaystyle \L\,\frac{x}{4}\,+\,\frac{y}{3}\,+\,\frac{y}{6}\,+\,\frac{x}{4}\:=\:\frac{x\,+\,y}{2}\) hours.


She walked from 7 AM to noon (5 hours): \(\displaystyle \L\,\frac{x + y}{2}\:=\:5\;\;\Rightarrow\;\;x\,+\,y\:=\:10\)


Since her total distance was: \(\displaystyle \L\,x\,+\,y\,+\,y\,+\,x\:=\:2(x\,+\,y)\) km

\(\displaystyle \;\;\)she walked:\(\displaystyle \L\,2(x\,+\,y)\:=\:2(10)\:=\:20\) km.