Deep in a hidden valley, Emek, Luna, and Nova reached a damaged sign pointing toward the expedition shelter. Their map showed two possible routes. Route A was 8.4 kilometers long, and they had already completed 2.4 kilometers of it. The remaining 6 kilometers crossed rocky ground where they could walk 2.4 kilometers per hour. Route B was 9.1 kilometers long, with 2.5 kilometers already completed. Its remaining 6.6 kilometers followed a smoother trail where they could walk 3 kilometers per hour. Emek calculated that Route A would take 2.5 more hours. Luna found that Route B would take only 2.2 hours, even though more distance remained. After comparing the travel times, they chose Route B. The smoother path carried them safely to the shelter before the valley grew dark.

Challenges

Challenge 1 of 5

Challenges

Challenge 1 of 4
Hint
Distance alone does not determine travel time. Compare distance divided by walking speed for each route.
Nova says Route A should be faster because only 6 kilometers remain, while Route B has 6.6 kilometers remaining. Which explanation best shows why Nova's reasoning is incorrect?
Route A is faster because 6 is less than 6.6.Route B is faster because 6.6 - 6 = 0.6 kilometer.Route B is faster because its walking speed is greater, giving 6.6 / 3 = 2.2 hours compared with 6 / 2.4 = 2.5 hours for Route A.Both routes take the same time because their remaining distances are close.
Correct! Route B has more distance remaining, but its faster walking speed makes its travel time shorter.
Not quite. Calculate the travel time for each route using remaining distance divided by walking speed.
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Hint
First find the difference between 2.5 hours and 2.2 hours. Then convert that difference to minutes.
Route A would take 2.5 more hours, while Route B would take 2.2 more hours. How many minutes of travel time did the group save by choosing Route B? Use 60 minutes in 1 hour.
Correct! Choosing Route B saves 18 minutes.
Try again. Find the difference in hours first, then multiply it by 60.
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Hint
Subtract the distance already completed from each total distance, then divide the remaining distance by the walking speed.
Emek wants to verify the map calculations before they continue. Which set of calculations correctly checks both the remaining distances and the travel times?
Route A: 8.4 + 2.4 = 10.8, then 10.8 / 2.4 = 4.5 hours; Route B: 9.1 + 2.5 = 11.6, then 11.6 / 3 = about 3.87 hoursRoute A: 8.4 - 2.4 = 6, then 6 / 2.4 = 2.5 hours; Route B: 9.1 - 2.5 = 6.6, then 6.6 / 3 = 2.2 hoursRoute A: 8.4 - 2.4 = 6, then 6 * 2.4 = 14.4 hours; Route B: 9.1 - 2.5 = 6.6, then 6.6 * 3 = 19.8 hoursRoute A: 8.4 - 2.4 = 6, then 2.4 / 6 = 0.4 hour; Route B: 9.1 - 2.5 = 6.6, then 3 / 6.6 = about 0.45 hour
Correct! These calculations verify both remaining distances and both travel times.
Not quite. Remaining distance is total distance minus completed distance, and travel time is remaining distance divided by speed.
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Gizli Vadiyi Geçmek
TR
ARC_G06_OPS_02_STORY_03
Gizli Vadiyi Geçmek
Crossing the Hidden Valley
EN
ARC_G06_OPS_02_STORY_03
Crossing the Hidden Valley