# Sarin’s family took a train part 12 (Math Question)

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The blog postings are about the Singapore Math. The readers can learn from the postings about Solving Singapore Primary School Mathematics. The blog presents the Math Concept, the Math Questions with solutions that teaches in Singapore Primary Schools. You or the kids will able to acquire knowledge of dealing with the Math Modeling, the Math Problem Solving and the Problem Sum from Lower Primary School to Upper Primary School level after read the blog postings. This posting is an upper primary school math question on Fraction, Ratio and Speed.

Read the posting on Sarin’s family took a train about Sarin’s family had their train ride from Singapore Tanjong Pagar Train Station.

Read the posting on about Sarin’s family venture in Kluang.

Read also the posting on Sarin learns rate of change in school (Math Concept) to learn about concept of Speed.

You can read the posting on Sarin learns concept of ratio in school to understand the concept of Ratio.

Read also the posting on Sarin learns the concept of Fraction (mathematics concept) to understand the concept of Fraction.

Challenge yourself with the question before look for the given solution‼!

Upper primary school mathematics question UPQ558

Sarin’s family took an express train left Singapore Woodlands Station for Kluang Station. At the same time, a normal train left Kluang Station for Singapore Woodlands Station. The average speed of the express train was 90 km/h more than that of the normal train. The express train and normal train took 4 hours and 10 hours to reach their destinations respectively, find the average speed of the express train and the distance of the two stations.

Solution:

The express train needs 4 hours to travel the same distance that the normal train needs 10 hours

Express train cover ¼ of the total distance per hour

Normal train cover 1/10 of the distance per hour

The difference in distance travel in fraction per hour = ¼ – 1/10 = 3/20

The speed is proportional to the distance,

The fraction in difference in speed = 3/20

Given the difference in speed is 90 km/h

3/20 ==> 90 km/h

1/4 ==> 90 × 5/3 = 150 km/h

The average speed of the express train is 150 km/h

The distance between the two stations = 4 × 150 = 600 km

Alternative solution(1):

The express train used 4 hours to travel the same distance that the normal need 10 hours From the model,

The difference per hour = 3 units

As speed proportional to distance,

3 units = 90 km/h

1 unit = 30 km/h

The speed of the express train = 5 ×30 = 150 km/h

The distance between the two stations = 4 × 150 = 600 km

Alternative Solution(2) :

The ratio of the number of hour to cover the distance,

Express : Normal = 4 : 10 = 2 : 5

The speed is inversely proportional to number of hours,

The ration of the speed,

Express : Normal = 5 : 2

The speed model, 3 units = 90 km/h

1 unit = 30 km/h

The speed of the express train = 5 × 30 = 150 km/h

The express train take 4 hour to reach Kluang Station,

The distance between the two stations = 4 × 150 = 600 km