Grades 9-10 Video Solutions 2024-2024_9-10

Video Transcription

Olivia walked in the park. She walked half of the total time at a speed of two kilometers per hour. She walked half of the total distance at a speed of three kilometers per hour.  She walked the rest of the time at a speed of four kilometers per hour. For what fraction of the total time did she walk at a speed of four kilometers per hour?  Let's denote the half of the time for Olivia's walk with t and the time she walks with a speed of four kilometers per hour with x.  Then the time she walks with a speed of three kilometers per hour is t minus x.  Then we have the following. At speed 2, time t, that gives us a distance of 2t. Speed 3, time t minus x, gives us a distance of 3 times t minus x.  Speed 4, time x, gives us a distance of 4x.  Then we know that 3t minus x equals 2t plus 4x because the distances are equal and that tells us that t equals 7x and x equals t over 7.  Therefore, we know that x equals 1 14th times 2t and then our answer is a.

Video Summary

Olivia's walk in the park involves three different speeds and time allocations. She walks half the time at 2 km/h and the rest at 3 km/h and 4 km/h. Calculations reveal that she walks a fraction \( \frac{1}{14} \) of the total time at 4 km/h.