Answered

Welcome to Westonci.ca, your go-to destination for finding answers to all your questions. Join our expert community today! Join our Q&A platform and get accurate answers to all your questions from professionals across multiple disciplines. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

PLS HELP

Pilar is playing with a motorized toy boat. She puts the boat in a lake and it travels 400m at a constant speed. On the way back to Pilar, the boat travels the same route at the same speed for 2 minutes, and then Pilar uses the remote control to increase the boat's speed by 10 m/min. So the return trip is 60 seconds faster. How long does the return trip take?

Sagot :

avaknrnk1

Answer:

7 minutes

Step-by-step explanation:

the trip takes 7 mins

Histrionicus

Pilar puts the boat in a lake that travels 400 meters at a constant speed. The time. On the return, the speed was the same for 2 minutes and then increase by 10m/min. The time boat takes in return back = 8 minutes

Solution for the time taken by speed change

The given information states that the away distance the boat traveled = 400 m

The time traveled at the same initial speed, v₁, by the boat on the way back = 2 minutes.

The increase in speed of the boat by Pilar =  10 m/min

The new speed, v₂ = v₁ + 10

The time for the return trip, t₂ = 60 seconds (1 minute) faster than the time for the trip, t₁

[tex]t_2 = t_i - 1[/tex]

Therefore we have;

[tex]v_i\times t_i = v_i \times 2 + v_2 \times (t_2-2) \\= 400\\v_i \times 2 + (v_i + 10) \times (t_2-2) = 400\\(v_i + 10) \times t_2 - 20 = 400\\[/tex]

but

[tex]v_i = \frac {400}{t} = \frac{400)}{t_2+ 1}[/tex]

Which gives;

[tex]\frac{(400) }{(t₂ + 1} + 10) \times t_2 - 20 = 400\\10\times ( t_2²+ 36·t_2-2)/(t_2+1) = 40010 \times t_2^²+ 10 \times t_2-420 = 0[/tex]

[tex]t_2^2+ t_2-42 = 0[/tex]

[tex](t_2 - 7)(t_2 + 6) = 0[/tex]

[tex]t_2 = 7[/tex] minutes or [tex]-6[/tex] minutes

Given that t₂ is a natural number, we have,

t₂ = 7 minutes

Whereby, [tex]t_2 = t_i - 1[/tex], we have;

[tex]7 = t_i - 1[/tex]

[tex]t_{i} = 1 + 7 = 8[/tex] Minutes

The trip normally takes 8 minutes

Learn more about speed and distance:

https://brainly.com/question/4931057

Thanks for using our platform. We're always here to provide accurate and up-to-date answers to all your queries. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.