1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Nat2105 [25]
3 years ago
7

On an uphill hike, Ted climbs at a rate of 3 miles an hour. Going down, he runs at a rate of 5 miles an hour. If it takes him 40

minutes longer to climb up than run down, what is the total length of Ted's hike?
Mathematics
2 answers:
andreyandreev [35.5K]3 years ago
6 0
Let the total length of Ted's hike be L and the total time spent be T.

The time spent going down is t, and the time spent going up is t+40 (if t is measured in minutes) or t + 2 hr/3 (if t is measured in hours).  Note that t + t + 2/3 must equal T, the total hiking time, with all measurerments in hours.

Distance uphill:  L = (3 mph)(t+2/3) = Distance downhill:  (5 mph)(t)

We need only find t, the am't of time req'd for Ted to go up to down.

3t + 2 = 5t, or 2 = 2t, or t = 1 (hour)

It will take Ted 1 hour to descend the hill and 1 2/3 hour to ascend the hill.

The total length of Ted's hike was then 2 2/3 hours, or 2 hours 40 minutes.

By the way, the distance in each direction is (5 mph)(1 hr) = 5 miles.  
77julia77 [94]3 years ago
6 0

Answer:

<h2>The total distance used by Ted was 10 miles, uphill and downhill.</h2>

Step-by-step explanation:

Givens:

  • Uphill hike: s=3\frac{mi}{hr}; (t+40)min
  • Downhill: s=5\frac{mi}{hr}; t min

So, Ted climbs the same distance in both directions, because it's the same trajectory, but at different speeds:

d_{uphill}=d_{downhill}

Applying the definition of a constant movement: d=st, we have:

3\frac{mi}{hr}(t+40)min=5\frac{mi}{hr}t min

However, we first need to transform the time in hours, because the speed is using hours in its unit. So, we know that 1 hour equals 60 minutes:

40min\frac{1hr}{60min}=0.67 hr

Therefore, the equation will be:

3\frac{mi}{hr}(t+0.67)hr=5\frac{mi}{hr}(t \ hr)\\3t+2=5t\\2=5t-3t\\2=2t\\t=\frac{2}{2}=1 \ hr

Therefore, downhill we took 1 hour, and uphill he took 1.67 hr or 1 hr and 40 min.

Now, we use this time to find the length of Ted's hike.

Uphill:

d_{uphill}=3\frac{mi}{hr}1.67 hr \\d_{uphill}=5mi

Downhill:

d_{downhill}=5\frac{mi}{hr}1 hr \\d_{uphill}=5mi

Therefore, the total distance used by Ted was 10 miles, uphill and downhill.

You might be interested in
Help me please !! give me right answer .
harina [27]

Answer:

2.04

Step-by-step explanation:

4 0
3 years ago
Brian invests £1500 into his bank account. He receives 2% per year simple interest. How much will Brian have after 3 years? Give
Jet001 [13]

Answer:

1590

Step-by-step explanation:

1500 x 0.02

= 30

30 x 3

= 90

1500+90 = 1590

(ps.. there was an equation for this i just forgot it, you can look it up and check it)

8 0
3 years ago
Find the distance between the two points in simplest radical form.<br> (3,9)and (0,2)
Aleks04 [339]

Answer:

7.62

Step-by-step explanation:

use distance formula

6 0
3 years ago
Please I want an before 2:00
Snezhnost [94]

Here's a photo of the solution. Hope it helps and please give brainlist!

6 0
2 years ago
1. Does the system of linear equations shown below have a solution? Explain.
Ira Lisetskai [31]

Answer:

hb      Step-by-step explanation:

4 0
3 years ago
Other questions:
  • Which of the following expressions is between 10 and 11? √10.5 √100 √21 √115
    11·2 answers
  • Multiply.
    13·2 answers
  • 5x - y ÷ 8 when x = 5 and y = 8
    8·2 answers
  • HELP, <br> Would I have to subtract 180 from 70 to get the answer for C?? What would the answer be?
    14·1 answer
  • Please help!! (question 5) struggling with revising for a math tests with is tomorrow
    5·2 answers
  • An internet search engine looks for a certain keyword in a sequence of independent web sites. It is believed that 20% of the sit
    7·1 answer
  • Pls helping giving lots of points :/
    6·1 answer
  • There are 225 calories in a 45 gram candy bar what is the unit rate​
    11·1 answer
  • Can someone please help me on this?? ill mark branliest for the best answer
    10·2 answers
  • For the past 16 months, susie has been paying $126.50 each month to her insurance company. after causing an accident last month,
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!