P6 Maths

baiyun SG

Thank you for your time

1) A dispatch rider has to deliver a parcel from City J to City S by a certain time. If he travels at an average speed of 96km/h, he will arrive at City S 1/3 hour (20mins) late. If he travels at an average speed of 90km/h, he will arrive at City S 1/2 hour (30mins) late. What is the distance between the two cities?

2) Ah Meng walks to school at an average speed of 4km/h everyday. One day, after walking a distance of 1km, he realised that his watch was slow. So, he ran at a constant speed and managed to reach the school just on time. Later, he calculated that if he had run at this speed right from the start of the journey, he would have reached school 5 minutes earlier.What was his running speed?

skythewood SG

Y is a box in the diagram

distance = time x speed

90km/h ====> distance = (Y + 1/2 hr) x 90

96km/h ====> distance = (Y + 1/3hr) x 96

since same distance, ( Y + 1/2 hr) x 90 = (Y + 1/3hr) x 96
( Y + 1/2 hr) x 15 = (Y + 1/3hr) x 16

in diagram form, YYYYYYYYYYYYYYY + (15 x 1/2hr)
YYYYYYYYYYYYYYYY + (16 x 1/3hr)

15/2hr = Y + 16/3hr
13/6hr = Y

90km/h ====> distance = (13/6 + 1/2 hr) x 90
= 240km

Oxide SG

I shall try to explain both(I've done the sums before)

as you've mentioned,1/3 h is 20 min and 1/2 h is 30 min.

30 min - 20 min =10 min (difference between time taken)

Now,for speed sums,a good way is to do ratio.Just remember,Speed is the reverse of Time and Speed is the same as Distance.

Let's do a ratio for speed first

Speed

90:96

15:16

Time

96:90

16:15

16u-15u=1u

1u - 10 min

15u - 150 min

=2.5 h

2.5 x 96km

240km

Ans:240km

In 1 hr, Ah Meng walks 4km.

In 15 min,Ah Meng walks 1 km.

Since he would have reached school 5 min earlier if had run at the running speed,

it means that he would take 5 mins less to travel 1km (if he runs at the running speed)

So,we take 15 min minus 5 min,

=10 min.

So at the running speed,he runs 1 km in 10 min.

So,at the running speed he runs 6km in 60 min

The running speed is 6 km/h

Although I am aware that the Maths PSLE is over already (am a candidate myself),I hope that this can help future PSLE students(if any).You may want to draw a diagram if you do not understand.