2019 · Q56
There are two parallel streets each directed North to South. A person in the first street travelling from South to North wishes to take the second street which is on his right side. At some place, he makes a 150° turn to the right and he travels for 15 minutes at the speed of 20 km/hr. After that he takes a left turn of 60° and travels for 20 minutes at the speed of 30 km/hr in order to meet the second street. What is the distance between the two streets?
Elementary MathematicsTrigonometry
- A7.5 km
- B10.5 km
- C12.5 km
- D15 km
Explanation
First leg: 15 min at 20 km/h = 5 km on a heading 150° from north; east component = 5·sin 150° = 2.5 km. After a 60° left turn the heading is 90° (due east), and the second leg is 20 min at 30 km/h = 10 km, all eastward. Separation of the parallel streets = 2.5 + 10 = 12.5 km.