Multiple choice

Two cyclists, Alice and Bob, start cycling towards each other from two different points on a straight road. Alice starts from Point A and cycles at a speed of 17 km/hr, while Bob starts from Point B and cycles at a speed of 13 km/hr. A butterfly rests on Alice's handlebar, while a dragonfly rests on Bob's handlebar. Both insects start flying towards each other from the moment the cyclists start in the same route. The butterfly flies at a speed of 27 km/hr, and the dragonfly flies at a speed of 30 km/hr. They meet each other and immediately return to their respective cyclists. They continue this pattern until the cyclists meet. If the distance between Point A and Point B is 20 km, what is the sum of the distances travelled by both butterfly and dragonfly?

  1. 28 km

  2. 18 km

  3. 38 km

  4. 42 km
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The cyclists meet after time t = Distance / (Speed1 + Speed2) = 20 / (17 + 13) = 20 / 30 = 2/3 hours. The insects fly at constant speeds (27 and 30 km/h) for the entire duration t. Total distance = (27 + 30) * (2/3) = 57 * (2/3) = 38 km.

AI explanation

Because the insects fly continuously until the cyclists meet, we calculate their total flying time using the relative speed concept. The cyclists approach each other at a relative speed of 17 plus 13, which is 30 km/hr. They cover the 20 km gap in 20 divided by 30 hours, which is 2/3 of an hour. The total flying speed of the butterfly and dragonfly is 27 plus 30, which is 57 km/hr. Multiplying this combined speed by the total time gives the total distance travelled: 57 multiplied by 2/3 equals 38 km.

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