Ask Singapore Homework?

Upload a photo of a Singapore homework and someone will email you the solution for free.



Question

primary 6 | Maths | Speed
No Answers Yet

Help Michelle! Anyone can contribute an answer, even non-tutors.

Answer This Question
Michelle
Michelle

primary 6 chevron_right Maths chevron_right Speed chevron_right Singapore

Please help to solve and explain. Thank you

Date Posted: 4 years ago
Views: 556
J
J
4 years ago
He didn't travel in the ½ hour he spent fixing the tire. He was expected to be travelling during that period at the previous speed.

3 + ½ = 3½

So this means he initially had 3½ h to complete the same remaining distance at the previous speed, such that he could arrive by 5pm.

But because of the burst tyre, he now has only 3 h to do so. In order to make up for lost time and reach at 5 pm, he had to go faster to cover the same remaining distance.


If he took 3 hours to complete the remaining journey, and travelled at 8.5km/h faster than before,

3 h x 8.5 km/h = 25.5 km

In 3 h, he travelled 25.5 km more than he would have at the previous speed.
Which also means at the previous speed, he would have travelled 25.5km less in the same 3 hours compared to the new speed

If he had gone at the previous speed for 3h he would still be 25.5km away from Batu Pahat at 5pm so he wouldn't reach in time.

So this 25.5 km was actually the distance he would have travelled in that ½ h at the previous speed, had there been no breakdown.

We can say that because of the breakdown, he was ½h behind schedule, and 25.5km further from Batu Pahat than expected at that point in time. So he needed to go faster to get back in schedule.


Since he would have travelled 25.5km in ½ h, his previous speed would be

(25.5 x 2) km/h = 51 km/h

Now had there been no tyre bursting,

4 h + 3½ h = 7½ h

He would have 7½ h to complete the whole journey.

(The tyre bursting happened 4 hours after the journey started , which means he had been travelling for 4 hours)

So total distance travelled
= 7½h x 51 km/h
= 382.5 km



Or

First 4 hours at 51 km/h
Last 3 hours at (51 + 8.5) km/h = 59.5 km/h

Total distance travelled
= 51 km/h x 4 h + 59.5 km/h x 3 h
= 204 km + 178.5 km
= 382.5 km
J
J
4 years ago
Alternative explanation :

If there was no tyre bursting , he would have 3½ h to complete it at the original speed.

Due to the bursting and delay caused by it,
he had only 3 h left to complete it. He uses a faster speed to do so.

New speed = original speed + 8.5km/h

Now we realise the distance travelled in both situations is the same.

Distance = speed x time

Let original speed be 1 unit
So new speed = 1 unit + 8.5

1 unit x 3½ = (1 unit + 8.5) x 3

3½ units = 3 units + 25.5

3½ units - 3 units km = 25.5

½ units = 25.5

1 unit = 25.5 x 2 = 51

So the original speed is 51 km.

The rest of the steps are the same as the first solution