Multiple choice

Lily and Emma decided to drive from their homes to a nearby beach for a weekend getaway. They both left at the same time, but due to different driving speeds, Emma arrived 15 minutes earlier than Lily. The ratio of driving speeds of Emma to Lily is 5 : 4, and the distance between their homes and the beach is 60 km. What is Lily's speed?

  1. 36 km/h

  2. 44 km/h

  3. 48 km/h

  4. 52 km/h

  5. 56 km/h
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C Correct answer
Explanation

Let speeds be 5x and 4x. Time taken by Emma = 60 / 5x = 12/x. Time taken by Lily = 60 / 4x = 15/x. Difference = 15/x - 12/x = 3/x. Given difference is 15 minutes = 0.25 hours. 3/x = 0.25 => x = 12. Lily's speed = 4x = 4 * 12 = 48 km/h.

AI explanation

Let the distance be 60 km, and use the formula time equals distance divided by speed. The time difference equals distance divided by the product of the speeds times the difference in the speed ratio terms. Plugging in the values, 15 divided by 60 equals the difference of the ratio terms (5 minus 4) multiplied by the product of the ratio terms (5 multiplied by 4) divided by a constant. This means 0.25 hours equals 60 multiplied by 1 divided by the constant, so the constant is 240. Multiplying the constant by Lily's ratio part of 4 gives Lily's speed as 48 km/h.

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