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Flo and Carl each must read a 500-page book. Flo reads one page every minute. Carl reads one page every 50 seconds. Flo starts reading at 1:00, and Carl starts reading at 1:30. When will Carl catch up to Flo?​​

Respuesta :

mhanifa

Answer:

  • Carl will catch up Flo at 4:00

Step-by-step explanation:

Given

  • Flo reads one page every minute
  • Carl reads one page every 50 seconds
  • Carl starts 30 minutes late
  • Max number of pages = 500

Let x be the number of pages each reads when Carl catches up Flo

Then we have the time for Flo and Carl

Flo:

  • x pages after x minutes

Carl:

  • x pages after 30 + x*50/60 minutes

The time is same:

  • x = 30 + 50/60x
  • x = 30 + 5/6x
  • x - 5/6x = 30
  • 1/6x = 30
  • x = 6*30
  • x = 180

180 minutes = 3 hours

1:00 + 3 hours = 4:00

[tex]\large\bold{\underline{\underline{Given:-}}}[/tex]

✭Flo and carl must read a 500 page book.

✭Flo reads one page every 1 minute (60seconds).

✭Carl reads one page every 50 Seconds.

✭Flo starts reading at 1:00.

✭Carl starts reading at 1:30.

[tex]\large\bold{\underline{\underline{To \: Find:-}}}[/tex]

When will carl catch up to flo?

[tex]\large\bold{\underline{\underline{Solution:-}}}[/tex]

Let Flo read certain pages when carl catches up with him. Then carl also read the same amount pages at that time.

Let the time passed be "x" minutes.

If carl Reads 1 page every 50 seconds, then 50 seconds can be written as 5/6th of a minute.

Carl's rate will be:

[tex]Carl \: \: Rate \: = \frac{Page}{Minutes} = \frac{ \frac{1}{5} }{6} = \frac{6}{5} [/tex]

Now, flo got a 30 minute head start. therefore, when carl catches up, he will read certain pages at x + 30 minutes.

And the number of pages that carl read after the time he had started, that is, "x" minutes will be:

[tex] ⇒\frac{6}{5} \times x[/tex]

But, the number of pages carl and flo read will be the same at that time!

[tex] ⇒\frac{6x}{5} = x + 30[/tex]

[tex] ⇒\frac{6x}{5} - x = 30[/tex]

[tex] ⇒\frac{x}{5} = 30[/tex]

[tex]⇒x = (30 \times 5) \: \: minutes[/tex]

[tex]⇒x = (150) \: \: minutes[/tex]

So carl catches up after 150 minutes.

Now, 1:30 + 150 minutes = 1.5 hours + 2.5 hours = 4:00.

Carl will catch up at 4:00.

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