Respuesta :
Step-by-step explanation:
distance = rate X time
5 minutes is 1/12 hr
f = full speed
28 km = f * 1/12 + 1/2 f * 1/12 + 1/4 f * 1/12
28 = f * (1/12 + 1/24 + 1/48)
28 = f * 7/48
f = 28 * 48/7 = 192 km/hr
Answer:
Full speed = 192 km/h
Step-by-step explanation:
- Let the speed be v km/h
- The speeds are given in intervals of 5 minutes starting with the first 5 minutes. Since there are 60 minutes in 1 hour,
5 minutes = 5/60 hour = 1/12 hour
- First five minutes(1/12 hour) is driven at full speed which is v km/h
Distance covered = v * 1/12 = v/12 km
- Second 5 minutes is driven at half speed which is v/2 km/h
Distance covered = v/2 * 1/12 = v/24 km - Last 5 minutes is driven at quarter speed which is v/4 km/h
- Distance covered = v/4 * 1/12 = v/48
- Total distance covered in terms of v
= v/12 + v/24 + v/48 [1]
- LCM of 12, 24 and 48 = 48
- Multiply each of the individual terms in [1] by 48/48 to get a common denominator
[tex]v/12 * 48/48 = v * 4/48 = 4v/48[/tex]
[tex]v/24 * 48/48 = v * 2/48 = 2v/48[/tex]
[tex]v/48 * 48/48 = v * 1/48 = 1v/48[/tex]
- Adding up we get the total distance covered (in terms of v):
[tex]\dfrac{4v}{48} + \dfrac{2v}{48} + \dfrac{1v}{48} \\\\= \dfrac{4v + 2v + 1v}{48}\\\\= \dfrac{7v}{48}[/tex]
- We are given the total distance traveled = 28km
Hence
[tex]\dfrac{7v}{48} = 28[/tex]
- Multiply both sides by [tex]\dfrac{48}{7}[/tex]:
[tex]\dfrac{7v}{48} \cdot \dfrac{48}{7} = 28 \cdot \dfrac{48}{7}[/tex]
or
[tex]v = 4 \cdot 48 \\\\v = 192 km/h[/tex]
