help!

bearsarebears SG

On a Saturday morning, Sue felt like getting some exercise. Sos he left home at 7am and walked to a shop along a flat road. When she reached the shop, she immediately 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 flat road, uphill and downhill were 4km/h, 3km/h and 6km/h respectively?

mhcampboy SG

what level is this question for?

mhcampboy SG

im not good at explaining. But here goes....

first find her average speed of the combined uphill and downhill journey.

Total hours she walk : 5

Flat slope : 4km/h
Upslope: 3km/h
Downslope : 6km/h

the problem is we dunno how much distance is upslope and downslope. but one thing we know she walked back the same route home. that means whatever distance she walk upslope, on the return trip, she walk downslope.

now let the slopping distance be Z km.
when she walk upslope, she used Z/3 hours. then downslope is Z/6 hours, same idea.

she walked the slopping distance 2 times, so she walked 2(Z) km of slope, upslope and downslope.

so average speed of all slopes is (total distance) / (total time)

total distance is 2 (Z) km

total time is (Z/3) hours + (Z/6) hours

So solution?

total time is 1/3( Z) hours + 1/6 ( Z) hours
which is 2/6 + 1/6 = 3/6 = 1/2 (Z) hours.

So total time is 1/2(Z) hours.

Now let's find average speed. Total distance / total time. The slope is Z km long.

She walked a Z km long sloping road 2 times.
So its 2(Z) km

Total Time : 1/2 (Z) hours

Divide total distance by total time

2( Z) km divide by 1/2( Z) hours

So the answer is 4km/hr

So average speed is 4km/hr. Z got cancelled already because both the distance and time contains Z.

her average speed on slope is 4km/h.
her speed on flat road is also 4km/h.'

So? Overall Speed is 4km/h.

She walks from 7 to 12 which is 5 hrs.

So answer for the question is..... 4km/hr times 5hrs which is 20 km

Answer is 20 km!!

Mr. Green

Hope you got it.... Laughing

bearsarebears SG

Thanks. How long did you took to get it? haha!

mhcampboy SG

About 20 mins... then spend my time how to elaborate .... i dun wan to give answers withour explaining... Laughing

but... u got it already prior to wad ive given u? or u just found out now?

bearsarebears SG

I got something like that.

Just got stumped cos I made a mistake in taking the average speed for up and down hill to be 4.5km/h..
then only had 2 equations relating to distance..
(Lack of 1 to completely solve the entire system)