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d1i1m1o1n [39]
3 years ago
15

Darnell and Hector ride their bikes at constant speeds. Darnell leaves Hector’s house to bike home. He can bike the 8 miles in 3

2 minutes. Five minutes after Darnell leaves, Hector realizes that Darnell left his phone. Hector rides to catch up. He can ride to Darnell’s house in 24 minutes. Assuming they bike the same path, will Hector catch up to Darnell before he gets home?
Mathematics
1 answer:
aksik [14]3 years ago
8 0

Answer:

yes

Step-by-step explanation:

Even after 5 minutes, it will still take Darnell 27 more minutes to get home. If Hector can make it in 24 minutes, then he can catch up to Darnell before he gets home.

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5x + 60y = 35

x +y = 1.5 : rewrite as x = 1.5-y   and substitute this formula for x in the first one:

5(1.5-y) + 60y = 35

distribute:

7.5 - 5y + 60y = 35

combine like terms:

7.5 + 55y = 35

subtract 7.5 from both sides:

55y = 27.5

divide both sides by 55 to solve for  y

y = 27.5 / 55 = 0.5

now substiute 0.5 for y in the 2nd equation:

x + 0.5 = 1.5

x = 1.5 - 0.5 = 1

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