I dont understand where the u comes from in theexplanation (part b). The solutio

Question

I dont understand where the u comes from in theexplanation (part b). The solution is hard to follow cananybody rework or advise? original question: "You drive from san antonio to houston, half the time at55km/h and the other half at 90km/h. On the way back you travelhalf the distance at 55 km/h and the the other half at 90km/h. Whatis your average speed A) from san antonio to houston B) fromHouston back to San Antonio C) the entire trip D) what is youraverage velocity?" I dont understand where the u comes from in theexplanation (part b). The solution is hard to follow cananybody rework or advise? original question: "You drive from san antonio to houston, half the time at55km/h and the other half at 90km/h. On the way back you travelhalf the distance at 55 km/h and the the other half at 90km/h. Whatis your average speed A) from san antonio to houston B) fromHouston back to San Antonio C) the entire trip D) what is youraverage velocity?"

Explanation / Answer

Let the distance between Houston to san Antonio be X For 1 st half : velocity v = 55 km / h distance x = X / 2 time t = x / v           = ( X /2 ) / 55           = X /110      ----( 1) For 2 nd half : ---------------- velocity v ' = 90 km / h distance x ' = X / 2 time t ' = x ' / v '            =( X/ 2 ) / 90            =X / 180         ----(2) Total distance = X total time T = t + t '                 = ( X / 110) + ( X / 180 )                 = 0.014646 X So, average speed V = X / T                                 = X / 0.014646 X                                 = 68.27 km / h

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