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igomit [66]
1 year ago
8

7.5.5. I usually walk from home to work. This morning, I walked for 10 minutes until I was halfway to work. I then realized that

I would be late if I kept walking. I ran the rest of the way. I run twice as fast as I walk. How many minutes total did it take me to get from home to work?
Mathematics
2 answers:
Oksi-84 [34.3K]1 year ago
8 0
It took five minutes to run the rest of the way because half of the way walking is 10 minutes and if you run twice as fast the other half of the way you will get to work in 5 minutes
olya-2409 [2.1K]1 year ago
3 0

Answer:

Given:

I usually walk from home to work. This morning, I walked for 10 minutes until I was halfway to work.

I then realized that I would be late if I kept walking.

I ran the rest of the way. I run twice as fast as I walk.

Find:

The number of minutes in total did it take me to get from home to work

Step-by-step explanation:

Had I kept walking, the second half of my trip would have taken 10 more minutes.

By doubling my speed for the second half of my trip,

I halved the amount of time it took me to finish.

So, the second half of my trip took 5 minutes, for a total trip time of  10+5 = 15 minutes.

The number of minutes in total did it take me to get from home to work is 15 minutes.

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63.5

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If one didn't take a 10 minute break he could drive 60 mph totalling 180 minutes but since he did and 180 - 10 = 170. He/she has to drive 180 miles in 170 min. so we take so we divde 180/170 and multiply by 60. If you round it to the nearest tenth you get 63.5

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| 9. The distance between Town A and Town B was 108 km. A car and a van left Town A at 12 00 for Town B. On reaching Town B, the
Westkost [7]

Answer:

a)  Time until both vehicles meet is 1.5 hours after starting at noon.  That makes it 1:30PM.

b)  Average speed of car is 84 km/h

Step-by-step explanation:

A -----------------------z------------B

          <u>Left</u>      <u>Speed(km/h)</u>      <u>Time</u>

Car:   12PM            X  

Van:   12PM           60

Car/Van

DistanceCar        AB + z

DistanceVan       Az

Ratio:                  (AB+z)/Az  = 7/5

Time until both meet = T (in hours)

Distance Car:            xT

Distance Van:           60T

====

  xT = AB + z

  60T = Az

---

(xT/60T)= (7/5)

x = 60(7/5)

x = 84 km/h

=====

Time for car to reach B is:    time (hr) = 108 km/(84 km/h)

                                                 time = 1.286 hours

Distance for at 1.289 hours is:    distance (km) = (60 km/h)*(1.286 h)

                                                   distance = 77.14 km

At 1.286 hours, the car reverses direction.  The van is (108 km - 77.14 km) or 30.86 km away.

Add the distances travelled by both vehicles after the car reverses direction at 1.286 hours.  The sum will be 30.86 km when they meet, at time of T.

Car Distance + Van Distance = 30.86 km

T(84 km/h) + t(60 km)

They meet when they are 0 km apart, which can be modeled with the following equation:

Van travel Distance - Car Travel Distance = 0 starting at 1.286 hr.

Let <u>t</u> be the time <u>after</u> 1.286 hours that both vehicles meet/collide.

t*(60 km/h)  +  t(84 km/h) = 30.86 km

t(60+84) = 30.86 km

t(144 km/h) = 30.86 km

t = 0.2143 hr

Total time until the car and van meet is 1.286 hr + 0.2143 hr for a total of 1.50 hours.

=================

a)  Time until both vehicles meet is 1.5 hours after starting at noon.  That makes it 1:30PM.

b)  Average speed of car is 84 km/h

==============

<u>CHECK</u>

Is the ratio of the distance travelled by the car and the van until they meet in the ratio of 7/5?

Car distance is (1.5 hr)(84 km/h) = 126 km

Van distance is (1.5 hr)(60 km/h) = 90.0 km

Ratio is 126/90 or 1.4

Ratio of 7/5 is 1.4

<u><em>YES</em></u>

     

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Remaining triangles B and D do not appear to be congruent.

Therefore, Options (B) and (D) will be the answer.

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