# Pilar is Playing With a Motorized Toy Boat

Pilar is Playing With a Motorized Toy Boat

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Shelly G.

Algebra

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## 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 style back to Pilar, the boat travels the aforementioned route at the same speed for 2 minutes, and so Pilar uses the remote control to increment the boat’due south speed past x g/min. And then the return trip is 60 seconds faster. How long does the return trip take?

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### Related Question

Pilar is playing with a motorized toy boat. She puts the gunkhole 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 aforementioned speed for 2 minutes, and and so Pilar uses the remote control to increment the gunkhole’s speed by x m/min. So the render trip is 60 seconds faster. How long does the return trip accept?

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### Video Transcript

come on hilarious playing with a motorized toy boat, Put it in the lake and travels 400 thousand at a constant speed. Nosotros’re modeling that here. 400 is equal to the whatever the rate is, times of time, we don’t actually know the rate or the time. So we’re leaving it as is on the mode back. The gunkhole travels the same road. Then I’g going to model the second trip hither, Same circular, which means information technology’southward still going 400 m At the same speed for two minutes. So we know whatsoever this charge per unit is, it’s going to be two times charge per unit for that rate. Notwithstanding, then pilar using the remote controller, increment the boat speed past 10. So nosotros’re doing here is nosotros’re going to take the charge per unit plus ten And then that’due south going to happen for. Information technology says here the return trip is 60 seconds faster, which ways it’s 1 minute faster. Well, here’s the matter if it’s one infinitesimal faster and it’s already been traveling for 2 minutes. The time that the boat is going, this increased speed, in that location’s really gonna be 3 minutes less than this time here. So this was the total amount of time from the original trip. Then we got two minutes and then T -3 is going to give me an overall i minute faster than that. Then to assistance with this, I’thousand going to if I want to solve for how long does the trip take that? I want to split both sides past T here. So that 400 over T. is equal to my are this is gonna assistance me because that can replace both of these. And then I’m gonna have an equation that I tin can solve for T. So 400 is equal to two, Multiplied past 400 over tea Plus 400 over tea plus 10 Times T -three. And so we tin can just multiply these together. And so we have 400-800 over tea. This I’m gonna have to distribute here. So 400 t. times negative three is going to be a negative 12 100 over tea. Then I’m going to have oh I forgot to do the this tea here first. And then that’s actually gonna be a plus 400 because these deaths will abolish out with that 1 That I take x times t. And x times a negative three is negative 30 there. Permit’due south combine my terms. I’m also going to subtract the 400 over. Okay, and then so I’k gonna put those two terms together. So I become 00 to a negative 400 over tea Plus x T -xxx. Now I want to become rid of the T. And my my denominator. So I’yard gonna multiply everything here Past PTI over one. I tin can do that considering I’m doing the same affair to the entire equation. So tee times 00 Michelle looks like a T. Okay this tea is gonna cancel out. So I got to make it a 400 plus 10 T squared minus 30 T. And I accept a quadratic. So I’m gonna rearrange that. So 10 t squared minus 30 mm hmm minus 400. And that’s divide everything now by 10. This will make information technology smaller numbers I need you to piece of work with. So zero is equal to T squared minus three T minus four. I tin can factor that. And so it multiplies. The negative four adds to 3 and negative three. And so information technology’s T minus four T plus one. I solve those individuals that become T. Equals positive for and T equals negative one. Well -1 does not represent a real time. So I don’t care almost that i. My answer hither is T. is iv. And that means that that was the original trip because I was this tea. And then the return trip Is going to exist one minute faster overall. And so it’south 4 -1 is equal to three minutes for the return trip.

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