Page 47 - Arithmetic

Worked Example 20
Two pipes can fill a tanker in 20 minutes and 24 minutes respectively. The cistern also has an external pipe. When all the three pipes are opened simultaneously, they can empty the tank in 15 minutes. How much time will the external pipe take to empty the tanker when operating individually? Solution:
Work done by the waste pipe in one minute
1111 =-(+)=−
152024 40
The minus sign indicates that the pipe is pouring out water. Therefore, the external pipe will take 40 minutes.
Time and Distance
REMEMBER:
You know that Distance = Speed × Time Time = 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒
𝑆𝑝𝑒𝑒𝑑
If the ratio of the speed of car A and B is in the ratio 1:2, the ratio of the time taken when both cars travel the same distance is 2:1.
If a man travels a certain distance at x miles per hour, and an equal distance at y miles per hour, the
average speed of the man for the entire journey = 2𝑥𝑦 miles per hour 𝑥+𝑦
Worked Example 21
June, a single mother, travels daily from her house to her kid’s school at a rate of 40 meters per second and walks back at a speed of 10 meters per second. If the entire journey takes 30 minutes, what is the distance between June’s house and the school?
Solution:
As June travels the same distance both ways, we can use the formula 2𝑥𝑦 meters per second 𝑥+𝑦
Average speed of June = 2×40×10 = 16 meters per second. 40+10
Time taken to travel the distance = 30 minutes = 1800 seconds Distance = Speed × time
= 16 × 1800 = 28,800 meters
Therefore, distance from school to house = 28800 = 14,400 meters 2
Page 46 of 55
Arithmetic Concept