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AMC 8 USA Math Olympiad

Time and Distance Problem from AMC 8: Problem 6 – 2018

Try this beautiful problem from AMC 8. It involves basic statistics and data representation. We provide sequential hints so that you can try the problem.

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What are we learning ?

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Competency in Focus: Time and Distance calculation

This problem from American Mathematics Contest 8 (AMC 8, 2018) is based on calculation of time and distance. It is Question no. 6 of the AMC 8 2018 Problem series.[/et_pb_text][et_pb_text _builder_version=”4.2.2″ text_font=”Raleway|300|||||||” text_text_color=”#ffffff” header_font=”Raleway|300|||||||” header_text_color=”#e2e2e2″ background_color=”#0c71c3″ custom_margin=”10px||10px||false|false” custom_padding=”10px|10px|10px|10px|false|false” border_radii=”on|5px|5px|5px|5px” box_shadow_style=”preset3″ inline_fonts=”Aclonica”]

First look at the knowledge graph:-

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Next understand the problem

[/et_pb_text][et_pb_text _builder_version=”4.2.2″ text_font=”Raleway||||||||” text_font_size=”20px” text_letter_spacing=”1px” text_line_height=”1.5em” background_color=”#f4f4f4″ custom_margin=”10px||10px” custom_padding=”10px|20px|10px|20px” box_shadow_style=”preset2″]On a trip to the beach, Anh traveled 50 miles on the highway and 10 miles on a coastal access road. He drove three times as fast on the highway as on the coastal road. If Anh spent 30 minutes driving on the coastal road, how many minutes did his entire trip take? $\textbf{(A) }50\qquad\textbf{(B) }70\qquad\textbf{(C) }80\qquad\textbf{(D) }90\qquad \textbf{(E) }100$[/et_pb_text][/et_pb_column][/et_pb_row][et_pb_row _builder_version=”4.0″][et_pb_column type=”4_4″ _builder_version=”3.25″ custom_padding=”|||” custom_padding__hover=”|||”][et_pb_accordion open_toggle_text_color=”#0c71c3″ _builder_version=”4.3.1″ toggle_font=”||||||||” body_font=”Raleway||||||||” text_orientation=”center” custom_margin=”10px||10px” hover_enabled=”0″][et_pb_accordion_item title=”Source of the problem” open=”on” _builder_version=”4.3.1″ hover_enabled=”0″]

American Mathematical Contest 2018, AMC 8 Problem 6

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Basic Time and Distance problem with an easy interpretation from AMC 8 – 2018 – Problem 6

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Start with hints 

[/et_pb_text][et_pb_tabs _builder_version=”4.2.2″][et_pb_tab title=”HINT 0″ _builder_version=”4.0.9″]Do you really need a hint? Try it first![/et_pb_tab][et_pb_tab title=”HINT 1″ _builder_version=”4.2.2″]Speed = \(\frac {distance}{time}\)  This can be the first hint for this sum. It is one of the important formula in science. Try to use it in this sum……..[/et_pb_tab][et_pb_tab title=”HINT 2″ _builder_version=”4.2.2″]So if we use the previous hint the speed would be  r = \(\frac {d}{t}\) so , r = \(\frac {10}{0.5}\)    r = 20 mph.[/et_pb_tab][et_pb_tab title=”HINT 3″ _builder_version=”4.2.2″]His speed on the highway then is $60$ mph. He drives $50$ miles, so he drives for $\frac{5}{6}$ hours, which is equal to $50$ minutes. Note : 60 miles\hour is equal to 1 mile\minute[/et_pb_tab][et_pb_tab title=”HINT 4″ _builder_version=”4.2.2″]I think you already got the answer but if not here is the last hint. The total amount of minutes spent on his trip is  =80 minutes[/et_pb_tab][/et_pb_tabs][/et_pb_column][/et_pb_row][/et_pb_section][et_pb_section fb_built=”1″ fullwidth=”on” _builder_version=”4.2.2″ global_module=”50833″][et_pb_fullwidth_header title=”AMC – AIME Program” button_one_text=”Learn More” button_one_url=”https://www.cheenta.com/amc-aime-usamo-math-olympiad-program/” header_image_url=”https://www.cheenta.com/wp-content/uploads/2018/03/matholympiad.png” _builder_version=”4.2.2″ title_level=”h2″ background_color=”#00457a” custom_button_one=”on” button_one_text_color=”#44580e” button_one_bg_color=”#ffffff” button_one_border_color=”#ffffff” button_one_border_radius=”5px”]

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