# Answer to Question #23367 in Mechanics | Relativity for jasmyne

Question #23367

John goes for a run. From his house, he jogs north for exactly 5.0 min at an average speed of 8.0 km/h. He continues north at a speed of 12.0 km/h for the next 30.0 min. He then turns around and jogs south at a speed of 15.0 km/h for 15.0 min. Then he jogs south for another 20.0 min at 8.0 km/h. He walks the rest of the way home.

How many kilometers does John jog in total?

How many kilometers does John jog in total?

Expert's answer

1. As John jogs north for exactly 5.0 min at an& average speed of 8.0 km/h, he jogged

D1 = 5.0[m]·8.0[km/h] = 1/12[h]·8.0[km/h] = 2/3[km]

north.

2. As John continued north at a speed of 12.0 km/h for the next 30.0 min, he moved

D2 = 30.0[m]·12.0[km/h] = 1/2[h]·12.0[km/h] = 6[km]

north.

3. As John jogs south at a speed of 15.0 km/h for 15.0 min, he moved

D3 = 15.0[m]·15.0[km/h] = 1/4[h]·15.0[km/h] = 3.75[km]

south.

4. As John jogs south for another 20.0 min at 8.0 km/h, he moved

D4 = 20.0[m]·8.0[km/h] = 1/3[h]·8.0[km/h] = 8/3[km]

south.

Therefore, John moved

DN = D1 + D2 = 2/3[km] + 6[km] = 20/3[km]

north and

DS = D3 + D4 = 3.75[km] + 8/3[km] = 77/12[km]

south. So, he needs to walk

D = |20/3[km] -& 77/12[km]| = 3/12[km]

to return home. But the question is about how many kilometers does John jog in total, so the answer is

D = DS + DN = 20/3[km] + 77/12[km] = 157/12[km].

D1 = 5.0[m]·8.0[km/h] = 1/12[h]·8.0[km/h] = 2/3[km]

north.

2. As John continued north at a speed of 12.0 km/h for the next 30.0 min, he moved

D2 = 30.0[m]·12.0[km/h] = 1/2[h]·12.0[km/h] = 6[km]

north.

3. As John jogs south at a speed of 15.0 km/h for 15.0 min, he moved

D3 = 15.0[m]·15.0[km/h] = 1/4[h]·15.0[km/h] = 3.75[km]

south.

4. As John jogs south for another 20.0 min at 8.0 km/h, he moved

D4 = 20.0[m]·8.0[km/h] = 1/3[h]·8.0[km/h] = 8/3[km]

south.

Therefore, John moved

DN = D1 + D2 = 2/3[km] + 6[km] = 20/3[km]

north and

DS = D3 + D4 = 3.75[km] + 8/3[km] = 77/12[km]

south. So, he needs to walk

D = |20/3[km] -& 77/12[km]| = 3/12[km]

to return home. But the question is about how many kilometers does John jog in total, so the answer is

D = DS + DN = 20/3[km] + 77/12[km] = 157/12[km].

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