32. Ethan cycled from home for r km at 9 km/h to the MRT station. He waited for 3 minutes before catching the next MRT train. The MRT train travelled at an average speed of 60 km/h. He walked for
2
km at an
Average speed of 6 km/h before reaching his school. The distance from his home to the school by the
above route is 12 km and the total time he spent is 28 minutes.
(Express, in terms of the time he spent cycling from home to the MRT station.
(ii) Find the distance he travelled on the MRT train.
(ii) Form an equation in and solve it.

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) = x%2F9

:

(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 = 5%2F12

Write a time equation

bike time + train time + walk time = 5/12 hrs

x%2F9 + %28%2811.5-x%29%29%2F60 + .5%2F6 = 5%2F12

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

HOPE IT HELP

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