SOLUTION: Ethan cycles from home for x km at 9km/h to the MRT station. He waited for 3 mins before catching the next MRT train. The MRT train travels at an average speed of 60km/h. He walks

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Question 800534: Ethan cycles from home for x km at 9km/h to the MRT station. He waited for 3 mins before catching the next MRT train. The MRT train travels at an average speed of 60km/h. He walks for 1/2km at an average speed of 6km/h before reaching his school. The distance from his home to the school by the above route is 12km and the total time he spent is 28 mins.
(i) Express, in terms of x, the time he spent cycling from home to the MRT station.
(ii) Find the distance travelled by Ethan when he was travelling to school using the MRT
(iii) Form an equation in x and solve it.
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
Ethan cycles from home for x km at 9km/h to the MRT station.
He waited for 3 mins before catching the next MRT train.
The MRT train travels at an average speed of 60km/h.
He walks for 1/2km at an average speed of 6km/h before reaching his school.
The distance from his home to the school by the above route is 12km and the total time he spent is 28 mins.
:
(i) Express, in terms of x, the time he spent cycling from home to the MRT station.
time = dist/speed
f(x) =
:
(ii) Find the distance travelled by Ethan when he was travelling to school using the MRT
dist by train
d = 12 - x - .5
d = 11.5 - x
:
(iii) Form an equation in x and solve it.
Subtract the 3 min of waiting, change to hrs: 25/60 =
Write a time equation
bike time + train time + walk time = 5/12 hrs
+ + =
multiply by 180, resulting in
20x + 3(11.5-x) + 30(.5) = 15(5)
20x + 34.5 - 3x + 15 = 75
20x - 3x + 49.5 = 75
17x = 75 - 49.5
17x = 25.5
x = 25.5/17
x = 1.5 km by bike
:
:
You can confirm this yourself, find the time of each stage of the trip and
the total should be 5/12 hrs which .4167 hrs on a calc