A woman cycles 30km in 1 hour 45 minutes. A part of her journey is on a level road 18km long, and the remaining journey is uphill. If the woman's average speed on the level road is 24km/h, what is her uphill speed (in km/h)?
- A20
- B15
- C12
- D10
Solution & Step-by-step Explanation
Given:
Total Distance =30km
Total Time =1 hour 45 minutes=1+
60
45
=1+
4
3
=
4
7
hours
Let's break down the journey into two parts:
Level Road part:
Distance
1
=18km
Speed
1
=24km/h
Time taken on level road (t
1
)=
Speed
1
Distance
1
=
24
18
=
4
3
hours
Uphill part:
Distance
2
=Total Distance−Distance
1
=30−18=12km
Time taken uphill (t
2
)=Total Time−t
1
=
4
7
−
4
3
=
4
4
=1 hour
Now, we compute the uphill speed:
Uphill Speed=
t
2
Distance
2
=
1 hour
12km
=12km/h
Total Distance =30km
Total Time =1 hour 45 minutes=1+
60
45
=1+
4
3
=
4
7
hours
Let's break down the journey into two parts:
Level Road part:
Distance
1
=18km
Speed
1
=24km/h
Time taken on level road (t
1
)=
Speed
1
Distance
1
=
24
18
=
4
3
hours
Uphill part:
Distance
2
=Total Distance−Distance
1
=30−18=12km
Time taken uphill (t
2
)=Total Time−t
1
=
4
7
−
4
3
=
4
4
=1 hour
Now, we compute the uphill speed:
Uphill Speed=
t
2
Distance
2
=
1 hour
12km
=12km/h