when they are both racing on hoverboards victoria is 3 times as fast as her brother.when she is on foot she is 3 times slower than her brother on his hoverboard. they took off on hoverboard at the same time but after 12 minutes Victoria's hoverboard broke and she immediately started to tun. if the race was a tie how long in minutes did it last from start to finish?
Answers
Answer:
answer of this question is that 9
Answer:
The time will be 48 minutes
Step-by-step explanation:
Let r be Max's rate of speed and t be the total time.
Using the equation d = rt for this situation
Victoria is 3 times as fast as Max so her part gives us the expression 3r(12)
For the remaining part of the race, Victoria is 3 times slower than Max. Lets represent it as 1/3r. Since we do not know the amount of time she travels this way so we will represent this as 1/3r(t-12)
Together the distance on hoverboard and the distance on foot can be represented by d=3r(12)+1/3r(t-12).
So we have
3r(12)+1/3r(t-12) = rt
Simplifying, we have
36r+1/3r(t)-1/3r(12) = rt
36r + 1/3rt - 12/3r = rt
36r + 1/3rt - 4r = rt
Combining all the like terms,
32r + 1/3rt = rt
Subtract 1/3rt from each side:
32r + 1/3rt - 1/3rt = rt - 1/3rt
32r = 2/3rt
Divide both sides by r we get
32r/r = (2/3rt)/r
32 = 2/3t
Divide both sides by 2/3 we get
32 ÷ 2/3 = 2/3t ÷ 2/3
32 ÷ 2/3 = t
32/1 × 3/2 = t
96/2 = t
48 = t
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