Distance speed time Maths problem

[yoriyori]

Please I need help with daughters Maths question...... If a train travels half the journey at 24km/hr and then 16km/hr the rest of the journey, and the journey takes 30mins, how far has it traveled?

Many thanks for your help

Yoriyori

[leanmeamum]

I think the distance would be 10 Kms.

Average speed is 20 Kms/hr
Time taken is 30 mins
So Distance = Speed X Time

20 X 0.5 (hours) = 10 Kms

Or

The train travels 20Kms in 1 hr so 1/2 the distance in 1/2 the time (Please don't use this because it's better to use the formula for accuracy, esp if calcs get complicated)

[Reading Mum]

half at 24 and half at 16 makes avg speed of 20km/hr. Journey is 1/2 hr so travels 10km

or

1/4 hr at 24km/hr travels 6km then 1/4hr at 16km/hr travels 4km so total travel is 10km

[yoriyori]

Thank you for your swift reply....

[999 mum]

If a train travels half the journey at 24km/hr and then 16km/hr the rest of the journey, and the journey takes 30mins, how far has it traveled?

Sorry to be pedantic, when there is reference to half the journey does the question clarify whether they are talking of journey time or distance?

[aliportico]

Yeah, you can't just take the mean of 16 and 24 to give an average speed of 20 km/h. Average speed = total distance/total time.

If it means half the journey by time, then Reading Mum's second method is the way to do it. Don't bring average speed into it

If it means half the journey by distance, it's a bit more complicated, probably beyond what would be expected of KS2, I think. (I made it 9.6km - anyone want to check that for me?)

[Guest55]

VERY poorly worded question ... impossible to attempt as it is not clear whether the 'half' refers to time or distance.

[WP]

If it means half the journey by distance, it's a bit more complicated, probably beyond what would be expected of KS2, I think. (I made it 9.6km - anyone want to check that for me?)

Easy to check: 4.8 km at 24 km/hr takes 0.2 hr, and 4.8 km at 16 km/hr takes 0.3 hr, total 0.5.

Deriving it needs a bit of algebra though, starting from d/(2*24) + d/(2*16) = 1/2.

[aliportico]

Giggle - I wasn't being entirely serious just a bit lazy! And yes, the algebra bit would be why I thought it was probably not required on a ks2 question? I imagine the question did say half the journey distance.

[leanmeamum]

If a train travels half the journey at 24km/hr and then 16km/hr the rest of the journey, and the journey takes 30mins, how far has it traveled?

Sorry to be pedantic, when there is reference to half the journey does the question clarify whether they are talking of journey time or distance?

I think the question is quite clear -

The train completes 1/2 the journey at a speed of 24km/hr & 1/2 at 16km/hr. The time & speeds are given & distance is needed. Because the distance travelled at each speed is 1/2 the total distance, therefore we can arrive at the average speed easily.

I'm saying this because km/hr is the distance traveled in an hour & 24 or 16 are the speed at which the train needs to move to cover a given distance in an hour.