PSLE 2012 — Bakery and library
A bakery and a library are 120 m apart. They are located between Hong's house and Jeya's house. The bakery is exactly half-way between the two houses. One day, Hong and Jeya started cycling from their houses at the same time and they arrived at the library together. Jeya cycled at 70 m per min while Hong cycled at a speed 15 m per min faster than Jeya.
- (a) How much further did Hong cycle than Jeya?
- (b) How far is Jeya's house from the library?
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The pattern behind it: Same time, same distance
Two travellers spend the same time, or cover the same distance.
In this one. Riding for the same length of time makes the two distances share one unit, so they are in the ratio of the speeds (70 : 85 = 14 : 17); the bakery being the mid-point puts the library 120 m off centre, which makes the two rides differ by 240 m — and that difference is exactly the 3-unit gap.
How to spot it
Two travellers set off together or one chases another, with constant speeds and a question about who is ahead, when they meet, or how far apart they are.
Common mistake
Children divide the whole distance by the difference in speed instead of dividing the gap between the travellers, or compare distances covered over different lengths of time.
Try one like it
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