Direction: A man travels from his home to a shop. At the shop, he purchases a…
2020
Direction: A man travels from his home to a shop. At the shop, he purchases a cylindrical jar with a capacity of 83,259 cm3. The numerical value of the distance from home to the shop, in kilometres, is seven more than one-third of the square root of one-eleventh of the jar’s capacity. The man’s speed, in km/h, is four times the numerical value of the time, in hours, taken to reach the shop. How many hours does the man take to reach the shop?
Answer: C. 3 — ConceptDistance equals speed multiplied by time: d = s × t. When speed is given as a multiple of time, substitute that relation into d = st and solve the…
- A.
3.5
- B.
2
- C.
3
- D.
2.5
- E.
4
Attempted by 35 students.
Show answer & explanation
Correct answer: C
Concept
Distance equals speed multiplied by time: d = s × t.
When speed is given as a multiple of time, substitute that relation into d = st and solve the resulting quadratic equation. A travel time must be positive.
Application
Let t be the time in hours and s be the speed in km/h. The given relation is s = 4t.
One-eleventh of the jar’s capacity is 83,259 ÷ 11 = 7,569.
Since √7,569 = 87, the distance is d = 7 + (1/3) × 87 = 7 + 29 = 36 km.
Using d = st gives 36 = (4t)t = 4t2, and therefore t2 = 9.
Time is positive, so t = 3 hours.
Cross-check
For t = 3 hours, s = 4 × 3 = 12 km/h, and 12 × 3 = 36 km, which matches the calculated distance.