Mathematics, 17.12.2019 16:31 YEOng

Abus travels 280km south along a straight path with an average velocity of 88km/h to the south. the bus stops for 24 min, then it travels 210 km south with an average velocity of 75 km/h to the south. what is the average velocity for the total trip?

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76.78 km/h To calculate the average velocity for the total trip, you need to first determine the total distance traveled and the total time taken. First, let's calculate the total distance traveled. The trip consists of 2 legs. The 1st leg is 280 km and the 2nd leg is 210 km. So the total distance is 280 km + 210 km = 490 km. Now you need to calculate the total time taken. For this problem, there are 3 intervals that need to be accounted for. The travel time for the 1st leg, the duration of the rest stop in the middle, and the travel time for the 2nd leg. The travel time for both legs is calculated by dividing the distance traveled by the average speed. So for the first leg we have 280 km / (88 km / h) = 3.181818 h The 2nd leg is 210 km / (75 km/h) = 2.8 h The rest stop in hours is 24 min / (60 min/h) = 0.4 h The total time is 3.181818 h + 2.8 h + 0.4 h = 6.381818 h The average velocity is the distance divided by the time, giving: 490 km / (6.381818 h) = 76.78 km/h

Answer from: montgomerykarloxc24x

The average velocity is calculated by dividing the total distance traveled by the total time. The average velocity of the total trip is 76.6km/h

Let

$d \to distance$

$t \to time$

$v \to velocity$

When the bus travels 280km with average velocity of 88km/h, the time spent is calculated as follows:

$v = \frac dt$

$88 = \frac{280}t$

Make t the subject

$t = \frac{280}{88}$

t = 3.2h

When the bus travels 210km with average velocity of 75km/h, the time spent is calculated as follows:

$v = \frac dt$

$75 = \frac{210}t$

Make t the subject

$t = \frac{210}{75}$

t = 2.8h

The total distance of the trip is:

d = 280km + 210km

d = 490km

The total time spent is:

t = 3.2h + 24min + 2.8h

Convert to hours

t = 3.2h + 24/60h + 2.8h

t = 3.2h + 0.4h + 2.8h

t = 6.4h

So, the average velocity (v) is:

$v = d \div t$

$v = 490km \div 6.4h$

v = 76.6km/h

Hence, the average velocity of the total trip is 76.6km/h

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